Question

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?

Answer 1

The number of possible groups or combination of three men can be formed from 10 is 120.

According to the given question.

Total number of men in a company, n = 10.

Number of men to be selected, r = 3

As we know that, What is a combination in math?

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A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Therefore, the number of possible groups or combination of three men can be formed from 10

= $^{10} C_{3}$

= 10!/ 3!7!

= 10(9)(8)/3(2)

= 5 × 3 × 8

= 120

The number of possible groups or combination of three men can be formed from 10 is 120.

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