Question

A classroom has 15 seats. The front row has 5 seats, the second row has 6 seats and the third row has 4 seats. 9 students are to be seated in the classroom.

a)In how many ways can they be seated?

b)3 of the students are short are short-sighted and must sit in the front row. The other students are free to sit anywhere. In how many ways can the students be seated?

Answer 1

a)

$N=C^9_{15}=\frac{15!}{9!6!}=5050$

b)

$N=C^3_5\cdot C^6_{10}=\frac{5!}{3!2!}\cdot\frac{10!}{6!4!}=10\cdot210=2100$