Answer to Question #146452 in Combinatorics | Number Theory for Josh

Question

A committee of 4 women and 2 men is to be selected from 10 women and 5 men. If two of the women \nare feuding and cannot serve on the committee together, in how many ways can the committee be selected?

a.2380

b.2100

c.280

d.1820

Answer 1

Committee of 4 women and 2 men is to be formed and two particular women(say A and B) are not to be together then there will be 3 cases

case 1)

2men, 4 women from (10-2) (excluding A and B both)

$$\dbinom{5}{2}\times\dbinom{8}{4}=10\times70=700$$

2men, A and 3 women from (10-2) (exclude B)

$$\dbinom{5}{2}\times\dbinom{8}{3}=10\times56=560$$

2men, B and 3 women from (10-2) (exclude A)

$$\dbinom{5}{2}\times\dbinom{8}{3}=10\times56=560$$

$$700+560+560=1820$$

d.1820