Question

A company is looking to fill its Board of Directors position. 3 positions will be for men, 2

Answer 1

Answer:

1764 ways

Step-by-step explanation:

Given:

Men = 9

Women = 7

Required Men: 3

Required Women: 2

'

Required

Total Possible Outcome

The total possible outcome can be determine as follows;

Total = (Selection of Men) and (Selection of Women)

Calculating Selection of Men;

Let n represent total number of men; This implies that n = 9;

Let r represent number of men to select; This implies that r = 3;

The selection can be done in the following ways;

$Male = nCr$

Where $nCr = \frac{n!}{r!(n-r)!}$

$Male = 9C3$

$Male = \frac{9!}{3!(9-3)!}$

$Male = \frac{9!}{3!(6)!}$

$Male = \frac{9 * 8 * 7 * 6!}{3!6!}$

$Male = \frac{9 * 8 * 7}{3!}$

$Male = \frac{9 * 8 * 7}{3*2*1}$

$Male = 84 ways$

Calculating Selection of Women;

Let n represent total number of men; This implies that n = 7;

Let r represent number of men to select; This implies that r = 2;

The selection can be done in the following ways;

$Female = nCr$

Where $nCr = \frac{n!}{r!(n-r)!}$

$Female = 7C2$

$Female = \frac{7!}{2!(7-2)!}}$

$Female = \frac{7!}{2!(5)!}$

$Female = \frac{7 * 6 * 5!}{2!5!}$

$Female = \frac{7 * 6}{2!}$

$Female = \frac{42}{2*1}$

$Female = 21 ways$

Recall that

Total = (Selection of Men) and (Selection of Women)

Hence,

$Total = 84 * 21$

$Total = 1764 ways$