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;
[tex]Male = nCr[/tex]
Where [tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
[tex]Male = 9C3[/tex]
[tex]Male = \frac{9!}{3!(9-3)!}[/tex]
[tex]Male = \frac{9!}{3!(6)!}[/tex]
[tex]Male = \frac{9 * 8 * 7 * 6!}{3!6!}[/tex]
[tex]Male = \frac{9 * 8 * 7}{3!}[/tex]
[tex]Male = \frac{9 * 8 * 7}{3*2*1}[/tex]
[tex]Male = 84 ways[/tex]
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;
[tex]Female = nCr[/tex]
Where [tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
[tex]Female = 7C2[/tex]
[tex]Female = \frac{7!}{2!(7-2)!}}[/tex]
[tex]Female = \frac{7!}{2!(5)!}[/tex]
[tex]Female = \frac{7 * 6 * 5!}{2!5!}[/tex]
[tex]Female = \frac{7 * 6}{2!}[/tex]
[tex]Female = \frac{42}{2*1}[/tex]
[tex]Female = 21 ways[/tex]
Recall that
Total = (Selection of Men) and (Selection of Women)
Hence,
[tex]Total = 84 * 21[/tex]
[tex]Total = 1764 ways[/tex]
