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

Answer:

A. C(30, 5)

Step-by-step 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.

$_{r}^{n}\textrm{C}=\frac{n!}{r!(n-r)!}$, 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,

$_{5}^{30}\textrm{C}=\frac{30!}{5!(30-5)!}$

$_{5}^{30}\textrm{C}=\frac{30!}{5!(25)!}$

$_{5}^{30}\textrm{C}=\frac{30*29*28*27*26*25!}{5*4*3*2*1*25!}$

$_{5}^{30}\textrm{C}=29*7*27*26$

$_{5}^{30}\textrm{C}=142506$

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)