Permutation And Combination
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  • 1. Permutation and Combination Probability -1
  • 2. Fundamental rule of Counting
    • If one operation can be performed in m different ways and another operation can be performed in n different ways ,then the two operations when associated together can be performed in m*n ways
  • 3. Factorial of n
    • The Continued product of first n natural Numbers is called factorial n and is denoted by n!
  • 4. Permutation
    • illustrates the number of ways to arrange elements in a definite order. The number of permutations of n elements of same kind taken r at a time.
  • 5. Example
    • Write down all the permutations of xyz.
    • xyz, xzy, yxz, yzx, zxy, zyx.
  • 6. Example
    • In how many ways can 3 of 8 different flowers be planted along one side of the road? nP r = 8P 3 = 336
  • 7. Example
    • .    Express  10 P 4  in terms of factorials.
    •     Solution .   10 P 4  =   10!  6!
  • 8. Combination
    • Combination illustrates the number of ways to arrange elements without a definite order. The number of combination of n elements taken r at a time.
  • 9. Example
    • In how many ways can a committee of 4 be selected from a group of 12 people? nC r = 12C 4 = 495
  • 10.
    • The number of combinations of 4 things taken 3 at a time.
    • We will denote this number as  4 C 3 .  In general,
  • 11. Problem
    •  1. Write all the combinations of abcd taken 1 at a time.
    • 2.Write all the combinations of abcd taken 2 at a time.
    • 3. Write their combinations taken 3 at a time.
    • 4. Write their combinations taken 4 at a time.
  • 12. Question No 1
    • What is the probability of getting 3 white balls in a draw of of 3 balls from a box contain 5 white and 4 black balls.
  • 13. Question no 2
    • A committee is to be constituted by selecting 3 people from a group consisting of 3 economists and 4 statistics find the probability that the committee consists of
    • Economists only
    • Two scientists
    • One economists and one statistician
  • 14. Question no 3
    • A sub committee of 6 members is to be formed out of group consisting of 7 men and 4 ladies. Obtain the probability that the sub committee will consist of
        • Exactly two ladies
        • Atleast 2 ladies
  • 15. Question no 4
    • A committee of 4people is to be appointed from 3 officers of the production department for offices of purchase department ,2 officers of sales department and one chartered accountant .find the probability of forming the committee in the following manner.
    • There must be one form each categories
    • It should have atleast one from the purchase department
    • The chartered accountant must be in the committee
  • 16. Question No 5
    • Twenty books are placed at random in a shelf. Find the probability that a particular pair of books shall be
    • 1) always together
    • 2) Never Together
  • 17. Question no 6
    • The letters of the word ‘failure’ are arranged at random . Find the probability that the consonants may occupy only odd positions