Answer to Question #218795 in Discrete Mathematics for ratnakar

Question

(a) In how many ways can a committee of 3 faculty members and two students be selected from 7 faculty members and 8 students

(b) How many ways are there to distribute 12 different books among 15 people if no person is to receive more than one book 

Answer 1

a)

$$\dbinom{7}{3}\dbinom{8}{2}=\dfrac{7!}{3!(7-3)!}\cdot\dfrac{8!}{2!(8-2)!}=35\cdot28=980$$

980 ways.

(b) Number of selecting people is 

$$\dbinom{15}{12}$$

12 books can be arranged among themselves in $12!$

Therefore the number of ways is

$$\dbinom{15}{12}\cdot12!=455\cdot479001600=217,945,728,000$$