Answer:
910
Step-by-step explanation:
From the given information;
Suppose that everyone served together;
Then, we have:
= C(8,3) × C(6,3)
= [tex]\dfrac{8!}{3!(8-3)!}\times \dfrac{6!}{3!(6-3)!}[/tex]
= [tex]\dfrac{8!}{3!(5)!}\times \dfrac{6!}{3!(3)!}[/tex]
= 1120
But since 1 man and 1 woman refuses to serve together;
Then:
The combination will be:
= C(7,2) × C(5,2)
= [tex]\dfrac{7!}{2!(7-2)!}\times \dfrac{5!}{2!(5-2)!}[/tex]
= [tex]\dfrac{7!}{2!(5)!}\times \dfrac{5!}{2!(3)!}[/tex]
= 210
∴
1120-210 = 910
Thus, the number of ways committee can be formed = 910
