1-A certain consulting firm employs 8 men and 4 women. In March, 3 employees are selected
at random to represent the company at a convention. What is the probability that the
representatives will NOT all be men?
A. 14/55
B. 3/8
C. 41/55
D. 2/3
E. 54/55

2-Jeffrey has a bag of marbles. The bag contains 6 red, 6 yellow, 12 green, and 12 blue marbles.
It contains no other marbles.
What is the probability that a marble chosen at random will be either red or yellow?
A. 1/6 B. 1/3 C. 1/2 D. 2/3 E. 3/4

3-A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and 3 different
pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3
days, what is the probability that he wears the same pair of shoes each day, but that no other
piece of clothing is repeated?
(1)(1/3)pow6(1/2)pow3
(2)(1/3)pow6(1/2)
(3)(1/3)pow4
(4)(1/3)pow2(1/2)
(5)5X(1/3)pow2
N.B: pow = power

4-A man is known to speak truth 3 out of 4 times. He throws die and reports that it is a 6. The
probability that it is actually a 6 is
A) 3/4
B) 5/8
C) 2/5
D) 3/5
E) 4/5

5-If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B,
C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of
4-letter code words?
A) 5 to 4
B) 3 to 2
C) 2 to 1 D) 5 to 1
E) 6 to 1

6-From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the
probability that equal numbers of boys and girls will be selected?
A. 1/10
B. 4/9
C. 1/2
D. 3/5
E. 2/3

7-If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the
probability that n(n + 1)(n+2) will be divisible by 8?
A. 1/4
B. 3/8
C. 1/2
D. 5/8
E. 3/4

8-A certain junior class has 1000 students and a certain senior class has 800 students. Among
these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If 1 student is
to be selected at random from each class, what is the probability that the 2 students selected will
be a sibling pair?
a) 3/40,000
b) 3/20,000
c) 1/32
d) 1/20,000
e) None of these

9-A string of 10 lightbulbs is wired in such a way that if any individual lightbulb fails, the entire
string fails. If for each individual lightbulb the probability of failing during time period T id 0.06,
what is the probability that the string of lightbulbs will fail during time period T?
A.0.06
B.(0.06)^10
C.1-(0.06)^10 D.(0.94)^10
E.1-(0.94)^10

10-At a certain business school, 400 students are members of the sailing club, the wine club, or
both. If 200 students are members of the wine club and 50 students are members of both clubs,
what is the probability that a student chosen at random is a member of the sailing club?
A. 1/2
B. 5/8
C. 1/4
D. 3/8
E. 3/5

11-A fair, six-sided die is rolled. What is the probability of obtaining a 3 or an odd number?
A. 1/6
B. 1/5
C. 1/4
D. 2/3
E. 1/2

12-On Saturday morning, Malachi will begin a camping vacation and I will return home at the
end of the first day on Which it rains. If on the first three days of the vacation the probability of
rain on each day is 0.2, what is the probability that Malachi will return home at the end of the
day on the following Monday?
A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

13-Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then
put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the
sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is
numbered 5 ?
A. 1/6
B. 1/5
C. 1/3 D. 2/5
E. 2/3

14-When tossed, a certain coin has equal probability of landing on either side. If the coin is
tossed 3 times, what is the probability that it will land on the same side each time?A.1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2

15-A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2 television
sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2
sets chosen will be a black-and-white set?
A. 1/7
B. 1/4
C. 5/14
D. 11/28
E. 13/26

16-If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the
probability that n(n + 1)(n + 2) will be divisible by 8?
A) 1/4
B) 3/8
C) 1/2
D) 5/8
E) 3/4

17-A bag contains 15 tickets, number from 1 to 15. A ticket is drawn and then another ticket is
drawn without replacement. Find the probability that tickets will show even numbers.
A) 1/5
B) 3/5
C) 4/5 D) 13/20
E) 2/5

18-2 people are to be selected from 10 people, which include male and female. Is the probability
that both them female greater than 1/2?
1) The number of females is greater than 5
2) The probability that both them are male is less than 1/10
A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question
asked.
B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question
asked.
C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is
sufficient alone.
D) Each statement alone is sufficient to answer the question.
E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is
needed to answer the statements.

19-A spider eats 3 flies a day. Until the spider fill its quota, a fly has 50% chance of survival if it
attempts to pass the web. Assuming 5 flies have already made the attempt to pass, what is the
probability that the 6th fly will survive the attempt.
a) 0 %
b) 25 %
c) 50%
d) 75%
e) 100%

20-A total of 9 women and 12 men reside in the 21 apartments that are in a certain apartment
building, one person to each apartment. If a poll taker is to select one of the apartments at random, what is the probability that the resident of the apartment selected will be a woman who
is a student?
(1) Of the women, 4 are students.
(2) Of the women, 5 are not students.
A`. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


Hints/Answers

1. [12C3-8C3]/12C3]
2. 1/3
3.(1/3)^6(1/2)^3
4. 3/4
5. 10P5:10P4 = 6:1
6. [3C2*3C2]/6C4
7. 3/8
8. 60/8,00000
9. (0.94)^10
10. 250/400
11. 1/2
12 .8*.8*.2
13 2/36
14 (1/2)^3
15. 13/28
16. 3/8
17. 1/2
18. try yourself
19. 50%
20. Try yourself

Learn 1! 2! 3! 4! 5! 6! 7! 8! 9! 10!

1. Evaluate 3!/0!
2. Write each if the following in factorial form:(i) 8.7.6/3.2.1(ii) (n+1)(n)(n-1)/3.2.1(iii) n(n-1)(n-2)....(n-r+1)
3. Evaluate 16P4
4. Find n nPr = n-1Pr + r. n-1Pr-1
5. How many signals can be given by 5 flags of different colours, using 3 flags at a time?
6. How many signals can be made with 4 different flags when any number of them are to be used at a time?
7. How many different 4-digits number can be formed out of digits 1,2,3,4,5,6 when no digit is repeated?
8. How many words can be formed from FASTING when no letter is repeated?
9. How many three digits can be formed by using each one of the digits 2,3,5,7,9 only once?
10. Find the numbers greater than 23000 that can be formed from the digits 1,2,3,5,6 without repeating any digit?
11. Find the numbers of 5 digits numbers that can be formed from the digits 1,2,4,6,8 (when no digit is repeated), but(i) the digits 2 and 8 are next to each other(ii) the digits 2 and 8 are not next to each other.
12. How many 6 digits numbers can be formed, without repeating any digit from the digits 0,1,2,3,4,5? in how many them will 0 be at tens place?
13. How many 5 digits multiples of 5 can be formed form the digits 2,3,5,7,9 when no digit is repeated?
14. In how many ways 8 books including 2 on English be arranged on a shelf in sucha way tat the English books are never together?
15. Find the number of arrangement of 3 books on English anf 5 books on Urdu for placing them on a shelf such that the books on the same subjects are together?
16. In how many ways can 5 boys and 4 girls be seated on a bench so that the girls and the boys occupy alternate seats?
17. How many words can be formed by MATHEMATICS
18. How many permutations of the word PANAMA can be made, If is to be the first letter in each arrangement?
19. How many numbers greater than 1000,000 can be formed from the digits 0,2,2,2,3,4,4?
20. 11 members of a club form 4 committes of 3,4,2,2 members so that no member is a member of more than one committee. Find the number of committees??
21. The D.C.Os of 11 district meet to discuss the law and order situation in their districts. In how many ways can they be seated in a round table, when two particular d.c.os insist on sitting together?
22. The governor of the punjab calls a meeting of 12 officers, in how many ways can they be seated at a round table?
23. Fatima invites 14 ppl to a dinner. there are 9 males and 5 females who are seated at two different tables so that guests of one sex sit one round table and the guests of the other sex at the second table. Find the number of ways in which all guests are seated?
24. Find the number of ways in which 5 men and 5 women are seated at a round table in such a way that no two persons of the same sex sit together?
25. Numbers of ways 4 keys can be arranged?
26. How many neclaces can be made form 6 beads?
27. Evaluate 20C17
28. Find n nC10 = 12 x 11 / 2!
29. Find n and r n-1Cr-1 : nCr : n+1Cr+1 = 3:6:11
30. How many diagonals triangles can be formed by joining vertices of the polygon having 8 sides
31. The no of members of a club are 12 boys and 8 girls. In how many ways can a committee of 3 boys and 2 girls be formed?
32. How many committee of 5 members can be chosen from a group of 8 persons when each committee must include 2 particular persons?
33. In how many ways can a hockey team of 11 players be selected out of 15 players? How many of them will include a particular player????
34. Show that 16C11 + 16 C 10 = 17C11
35. There are 8 men and 10 women members of a club. How may committees of   can be formed(i) 4 women(ii) at the most 4 women(iii) atleast 4 women
36. There are 5 green 3 red in a box one ball is taken out probabilty the ball is green? the ball is red?
37. Is sample spaces = { 1,2,3,....9}, Event A= {2,4,6,8} and Event B= {1,3,5} find P(AUB)
38. The box contains 10 red, 30 white and 20 black marbles. A marble is drawn at random. Find prob that its is either red or white?
39. A natural no is chossen out of first 50 natural numbers. what is the prob that the chosen no is multiple of 3 or 5
40. A card is drawn from a deck of 52 playing cards. What is prob that its diamond or ace?
41. A die is thrown twice. prob that sum of dots be 3 or 11?
42. There are 10 girls and 20 boys in a class. Half of the boys and half of the girls have blue eyes. Find the prob that one student chosen as a monitor is either a girl or has blue eyess..
43. The number of rainy days in Murree durng the month of July for the past ten years are 20,20,22,22,23,21,24,20,22,21?? Estimate the prob of rain falling on a particular day of july. hence find the number of days in which picnic programme can be made by a group of students who wish to spend 20 days in Murree?
44. The prob that a person A l b alive 15 yrz hence is 5/7 and another person B el b alive 15 yrz hence is 7/9, Find the prob that both el b alive 15 yrz hence?
45. two coins are tossed twice each. find the prob that the head appears on forst toss and the same faces appear in the two tosses?
46. Two cards from a deck of 52 cards are drawn in sucha way tat the card is replaced afta the frst draw. Fin prob i) first card is KING second is QUEEN ii) both the cards are faced cards i.e king queen jack
47. A fair dice is thrown twice. Find prob that a prime no of dots appear in frst throw and the numbers of dots in the second throw is less than 5?
48. A bag contains 5 white 7 black 8 red balls are drawn 4m bag. what prob that the first ball is red, second is white, and third is black, when every time the ball is replaced??

MCQ's from Chapter 3 Matrices and Determinants Mathematics book 1 for FSC pre engineering and pre medical for Board of Intermediate and Secondary Education. Also For Entry Test Preparation for UET, NUST, PIEAS, GIKI, AIR, FAST, WAH University, UHS, other engineering Universities and Medical Colleges. 

MCQ's from Chapter 1 Number systems Mathematics book 1 for FSC pre engineering and pre medical for Board of Intermediate and Secondary Education. Also For Entry Test Preparation for UET, NUST, PIEAS, GIKI, AIR, FAST, WAH University, UHS, other engineering Universities and Medical Colleges.