Question

Scott has eight CDs, and he picks two to take to work each day. How many different ways can Scott choose two CDs?

a.)56 B.)28 C.)20,160 D.)112

Answer 1

Correct answer is B.

$C^8_2= \frac{8\times 7}{2\times 1}=28$

Answer 2

Answer:

The correct option is B.

Step-by-step explanation:

The total number of CDs is 8.

The number CDs Scott choose is 2.

We have to find the number of different ways that Scott can choose two CDs.

The formal of combination for selecting r objects from n is distinct object is

$^nC_r=\frac{n!}{r!(n-r)!}$

Scott select 2 CDs from 8 CDs, so the total number of ways is

$^8C_2=\frac{8!}{2!(8-2)!}$

$^8C_2=\frac{8!}{2!6!}$

$^8C_2=\frac{8\times 7\times 6!}{2\times 1\times 6!}$

Cancel out the common factors.

$^8C_2=\frac{8\times 7}{2}$

$^8C_2=28$

The total number of ways to select 2 CDs from 8 CDs is 28. Therefore option B is correct.