Question

a textbook search committee is condisdering 10 books for possible adoption. The committee has decided to select 5 of the ten for further consideration. in how many ways can it do so

Answer 1

Answer:

They can do so in 252 ways.

Step-by-step explanation:

The order in which the books are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

5 books from a set of 10. So

$C_{10,5} = \frac{10!}{5!(10-5)!} = 252$

They can do so in 252 ways.

Answer 2

Answer:

∴ Number of ways to select 5 books from 10 books for adoption is 252 .

Step-by-step explanation:

A Permutation is an ordered Combination. When the order does matter it is a Permutation. There are basically two types of permutation:

• Repetition is Allowed: such as  above. It could be "555".

• No Repetition: for example the first three people in a running race. You can't be first and second.

Formula is given by:

$nC_r= \frac{n!}{r! (n-r)!}$, where n is the number of things to choose from,  and we choose r of them,  no repetitions,  order matters. Here , n=10 , r=5.

⇒ $10C_5 = \frac{10!}{5!(10-5)!}$

⇒ $10C_5 = \frac{10!}{5!(5)!}$

⇒ $10C_5 = 252$

∴ Number of ways to select 5 books from 10 books for adoption is 252 .