Permutation And Probabilty

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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??