Answer: 2863
Step-by-step explanation:
Given : The number of UCF students = 7
The number of UF students = 8
If a committee of 4 people to be formed , then the number of ways to form the committee such that every committee must have at least one UCF student is given by :-
[tex]^7C_4\cdot ^8C_0+^7C_3\cdot ^8C_1+^7C_2\cdot ^8C_2+^7C_1\cdot ^8C_3\\\\=\dfrac{7!}{4!(7-4)!}\times1+\dfrac{7!}{3!(7-3)!}\times \dfrac{8!}{1!(8-1)!}+\dfrac{7!}{2!(7-2)!}\times\dfrac{8!}{2!(8-2)!}+\dfrac{7!}{1!(7-1)!}\times\dfrac{8!}{3!(7-3)!}\\\\=35+280+588+1960=2863[/tex]
Hence, there are 2863 ways to form the committee which must have at least one UCF student .
