Question

a committee consisting of 4 faculty members and 5 students is to formed. every committee position has the same duties and voting rights. there are 10 faculty members and 14 students eligible to serve on the committee. in how many ways can the committee be formed

Answer 1

25C4= (25!)/(4!*(25-4)!)=(25!)/4!*21!= (21!* 22*23*24*25)/(1*2*3*4*21!)= 12650

Explanation:

Answer 2

For the faculty we have 10 choose 4 and for the students we have 14 choose 5, so total combinations of

`\displaystyle {10 \choose 4}{14 \choose 5} = (10 \cdot 9\cdot 8 \cdot 7)/(4 \cdot 3 \cdot 2 \cdot 1) \cdot (14 \cdot 13\cdot 12 \cdot 11 \cdot 10)/(5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)`

`\quad= ( 10(3)(1)(7) )(14(13)(1)(11)(1)) = 210(2002) = 420420`

Answer: 420,420