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

D. 1960

Explanation:

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

• 
  `\huge=(7!)/(3!.(7-3)!)`

• 
  `\huge=(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=(8!)/(5!.(8-5)!)`

• 
  `\huge=(8!)/(5!.3!)`

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

• 
  `\huge=(8.7.6)/(3.2.1)`

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

• = 1960