Question

Statistics

During an extended vacation, you plan to read 3 books out of the 10 on your shelf that you've been meaning to read. How many different groups of 3 books might you take with you to read on vacation?


answer choices:

120.

720.

1,000.

30.

Answer 1

120

Explanation:

The number of ways to select
`r` things from a group of
`n` things is given by the combination formula.

`nCr=(n!)/(r!(n-r)!)`

Where n! means n*(n-1)*(n-2)....

• There are 10 total books, so n = 10
• you have to choose 3 books, so r = 3

Plugging these into the formula gives us:

`10C3=(10!)/(3!(10-3)!)=(10*9*8*7*6*5*4*3*2*1)/((3*2*1)(7*6*5*4*3*2*1))=(10*9*8)/(3*2*1)=120`

Hence, there can be 120 different groups of 3 books that u can choose from 10 books total.