Question

Of the 15 novels written by a certain author, 8 were mysteries, 6 were romances, and 1 was a fantasy novel. The books were placed in groups of 6

How many groups of 6 books may be formed?




B) How Many groups of 6 will consist of all mystery books?





C) What is the probability that a group picked at random will consist of all mystery books?





D) What is the probably that a group, picked at random , will consist of 3 mysteries,

2 romances and 1 fantasy?





E) What is the probability the group of 6 will consist of all fantasy books?

Answer 1

A) 3603600

B) 40320

C) 0.0112

D) 1.86 × 10^-15

E) 0

Explanation:

Given the total number of books to be 15 novels

A) How many groups of 6 books may be formed?

This will be 15 permutation 6

15P6 = 15!/(15 - 6)!

= 3603600 groups

B) How Many groups of 6 will consist of all mystery books?

This will be 8 factorial

8! = 40320

C) What is the probability that a group picked at random will consist of all mystery books?

This will be

8! ÷ 15P6 = 40320 ÷ 3603600

= 0.0112

D) What is the probably that a group, picked at random , will consist of 3 mysteries, 2 romances and 1 fantasy? This means

8C3/15P6 × 6C2/15P6 × 1C1/15P6

0.00016 × 0.000042 × 0.00000028

1.86×10^-15

E) What is the probability the group of 6 will consist of all fantasy books?

The probability is approximately equal to zero.

E) What is the probability the group of 6 will consist of all fantasy books?