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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!

Respuesta :

Greenleafable
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)


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.

[tex]_{r}^{n}\textrm{C}=\frac{n!}{r!(n-r)!}[/tex], where,

[tex]n=\text{Total number of items}[/tex],

[tex]r=\text{Number of items being chosen at a time}[/tex]

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

[tex]_{5}^{30}\textrm{C}=\frac{30!}{5!(30-5)!}[/tex]

[tex]_{5}^{30}\textrm{C}=\frac{30!}{5!(25)!}[/tex]

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

[tex]_{5}^{30}\textrm{C}=29*7*27*26[/tex]

[tex]_{5}^{30}\textrm{C}=142506[/tex]

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