Question #146452

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


1
Expert's answer
2020-12-01T02:55:23-0500

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)


(52)×(84)=10×70=700\dbinom{5}{2}\times\dbinom{8}{4}=10\times70=700

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


(52)×(83)=10×56=560\dbinom{5}{2}\times\dbinom{8}{3}=10\times56=560

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


(52)×(83)=10×56=560\dbinom{5}{2}\times\dbinom{8}{3}=10\times56=560

700+560+560=1820700+560+560=1820

d.1820



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