Question

in how many ways a group of 4 men and 3 women be made out of a total of 8 men and 5 woman​

Answer 1

Answer:

700 ways

Step-by-step explanation:

4 men out of 8 men can be selected in 8C4 ways

3 women out of 5 women can be selected in 5C3 ways

Total no of ways = 8C4 x 5C3

T = 8!/4!4! x 5!/3!2!

= 70x10 = 700 ways

Answer 2

Given,

Number of men = 8

Number of women = 5

To find,

Number of ways in which we can make a group of 4 men and 3 women out of 8 men and 5 women.

Solution,

Now , we need to make sure that a group has 4 men and 3 women.

Let's select 4 men first,

Number of ways to select 4 men out of 8 men = ${}^{8}C_{4}$ = $\frac{8!}{4!(8 - 4)!} = \frac{8!}{4!(4)!} = \frac{8*7*6*5}{4*3*2*1} = 70$

= 70 ways

Number of ways to select 3 women out of 5 women = ${}^{5}C_{3}$ = $\frac{5!}{3!(5 - 3)!} = \frac{5!}{3!(2)!} = \frac{5*4}{2} = 10$

= 10 ways

Therefore number of ways to make a group of 4 men and 3 women out of 8 men and 5 women = ${}^{8}C_{4}$ x ${}^{5}C_{3}$ = 70 x 10 = 700 ways

Hence, we can make a group of 4 men and 3 women out of 8 men and 5 women in 700 ways.