Question

A textbook search committee is considering 13 books for possible adoption. The committee has decided to select 3 of the 13 for further consideration. In how many ways can it do​ so?
11.8 #8

Answer 1

Number of ways in which the 3 can be selected from 13  = 286

Step-by-step explanation:

Step 1:

Number of books considered by the textbook search committee = 13

Number of books selected from this 13 = 3

We need to determine number of ways in which the 3 can be selected from the 13

Step 2 :

The order of the 3 books selected does not matter. So,

Number of ways in which the 3 books can be selected from 13 books =  C(13,3) = $\frac{13!}{10! . 3!}$

                                                                                             =$\frac{ 13 . 12 .11 . 10!}{10! . 3! }$

                                                                                             =$\frac{1716}{6}$ = 286

Step 3 :

Answer :

Number of ways in which the 3 can be selected from 13  = 286