Question

5. Discuss the difference between permutations and combinations. Make up an example of each

and work out the solutions.

Answer 1

#Solution:

1)

A permutation is an arrangement in which definite order of a number of objects taken some or all at a time. The formula of Permutation:

nPr = n!/(n-r)! , where

The Number of permutations of n different objects taken r at a time.

Example: Number of 4-digits number can be formed by using the digit 1 to 9 if repetition of digits is not allowed.

n = 9

2)

Combinations: A combination If we have n objects and we want to choose r  of them, we can find the total number of combinations by using the following formula:

The formula of Combination is:

nCr = n!/[r!(n-r)!] , where

Example: Number of 4-digits number can be formed by using the digit 1 to 9 if repetition of digits is not allowed.

n = 9

r = 4

9P4 = 9!/(9-4)! = 9!/5! = (9 X 8 X 7 X 6 X 5!) / 5! = 9 X 8 X 7 X 6 = 3024