Question

Carey has 30 CDs and wants to take pick out 5 to put into her CD player. How many different combinations of CDs can she pick out?

C(30, 5)
C(25, 5)
30!

Answer 1

A. C(30, 5)

Explanation:

We have been given that Carey has 30 CDs and wants to take pick out 5 to put into her CD player. We are asked to find the number of different combinations of CDs can she pick out.

We will use combinations to solve our given problem.

`_(r)^(n)\textrm{C}=(n!)/(r!(n-r)!)`, where,

`n=\text{Total number of items}`,

`r=\text{Number of items being chosen at a time}`

Upon substituting our given values in above formula we will get,

`_(5)^(30)\textrm{C}=(30!)/(5!(30-5)!)`

`_(5)^(30)\textrm{C}=(30!)/(5!(25)!)`

`_(5)^(30)\textrm{C}=(30*29*28*27*26*25!)/(5*4*3*2*1*25!)`

`_(5)^(30)\textrm{C}=29*7*27*26`

`_(5)^(30)\textrm{C}=142506`

Therefore, Carey can pick 5 CDs from 30 CDs in
`_(5)^(30)\textrm{C}=142506` ways and option A is the correct choice.

Answer 2

The correct answer is C(30,5)

That's because you have to know factorials and apply the formulas to find out that:
30! / [5!(30 - 5!)]
30! / (5! * 25!), which means that there are 142506 combinations, or C(30,5)