Question

A professor wants to arrange his books on a shelf. he has 30 books and only space on the shelf for 20 of them. how many different 20-book arrangements can he make using the 30 books? this is an example of a problem that can be solved using which method?

Answer 1

Answer: Total arrangement are 30045015

Given problem will be solved with help of combination.

Explanation:

When we find the arrangement in which the order does not matter then we use combination,

Here, we have to find the possible arrangement in which order does not matter,

Thus, we will use combination to find the answer.

Here the total number of books = 30

A self contains, the number of book = 20,

Hence, the total arrangement of 20 books out of 30 books

`=^(30)C_(20)`

`=(30!)/(20!(30-20)!)`

`=(30* 29* 28* 27* 26* 25* 24* 23* 22* 21)/(10!)`

`=(4.9557887* 10^(12) )/(3628800 )=30045015`

Answer 2

This is an example of a problem that can be solved using combination.

The number of possible arrangements is

`P\left(30,20\right)=(30!)/(\left(30-20\right)!* 20!)=30,045,015`

There are 30,045,015 possible 20-book arrangements.