Question

Permutations and, combinations: problem type 2.

(A) From a collection of 51 store customers, 3 are to be chosen to receive a special gift. How many
groups of 3 customers are possible?

(B) How, many different committees of size 4 can be formed from 14 people ?

Answer 1

Explanation:

Permutations:

nP r = n!/(n + r)!

Combinations:

nCr = n!/(n - r)!r!

c - combination

p - permutations

Since in both the problems they are looking for different groups, it is a combination problem. the order in which the people were selected in each group is not important, what is required are different groups.

A.

n = 51

r = 3

51C 3 = 51! / ((51 - 3) ×3!)

51C3 = 20 825 groups

OR:

`c = (51)/(3) * (50)/(2) * 49`

`c = 20825`

B.

`c = (14)/(4) * (13)/(3) * (12)/(2) * 11`

`c = 1001`