Question

How many ways are there to choose 3 men and 5 women from groups of 7 men and 8 women?

A. 840
B. 1411200
C. 91
D. 1960

Answer 1

Answer:

D. 1960

Step-by-step explanation:

• Number of ways to choose 3 out of 7 men $= C^7_3$

• $\huge=\frac{7!}{3!.(7-3)!}$

• $\huge=\frac{7!}{3!.4!}$

• $\huge=\frac{7.6.5.\cancel{4!}}{3.2.1.\cancel{4!}}$

• $\huge=35$

• Number of ways to choose 5 out of 8 women $= C^8_5$

• $\huge=\frac{8!}{5!.(8-5)!}$

• $\huge=\frac{8!}{5!.3!}$

• $\huge=\frac{8.7.6.\cancel{5!}}{\cancel{5!}.3!}$

• $\huge=\frac{8.7.6}{3.2.1}$

• $\huge=56$
• Total no. of ways of choosing the committee = 35*56

• = 1960