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

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)


"\\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



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