Question

A disc jockey can select 4 records from 10 to play in one segment. How many ways can this selection be done if order doesn’t matter

Answer 1

`C(10,4)=10C_4=210`

Explanation:

A combination is an arrangement where the order is not important. Mathematically, a combination is the number of different groups of "
`n`" elements that can be formed from an initial group of "
`k`" elements. It's calculated with the following formula:

`C(n,k)=nC_k=(n!)/(k!(n-k)!)`

Where:

`k\leqslant n`

In this case:

`n=10\\k=4`

Therefore the number of ways that the disc jockey selction can be done is:

`C(10,4)=10C_4=(10!)/(4!(10-4)!) =(10!)/(4!(6!))=210`