Question

Compute the permutations and combinations. A company has 10 men qualified to run a machine that requires 3 operators at a time. Find how many groups of 3 operators are possible. 240 720 120

Answer 1

120

Explanation:

To solve this question we would be using combination formula.

The formula for combination is given as:

C(n, r) = nCr

nCr = n!/r! ×(n - r)!

In the above question,

n = 10 men

r = 3 operators

Hence,

nCr = n!/r! × (n - r)!

10C3 = 10! /3! × (10 - 3)!

10C3 = 10!/3! × 7!

10C3 = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 /(3 × 2× 1 ) ×(7 × 6 × 5 × 4 × 3 × 2 × 1)

10C3 = 10 × 9 × 8 / 3 × 2× 1

10C3 = 720/6

10C3 = 120

Therefore, the number of groups of 3 operators that are possible is 120.