Question

Jill has six different books. She will select one book on Monday and a different one to read on Wednesday. In how many ways can Jill select two different books?
A. 36
B. 30
C. 18
D. 15
E. 12

Answer 1

Answer:

D. 15

Step-by-step explanation:

For this case we can begin finding the number of ways in order to select two different books for Monday and Wednesday. We know that Jill can select a book on Monday in six different ways snce she has a total of 6 books. And for Wednesday, she need another book so then can select any of the five remaining books, and the total number of ways would be:  

N= 6 × 5 = 30 ways.

We are going to assume that the order no matter. If she select a book A and then another B is the same if she select first the book B and then the book A. We are interested inthe possible pairs, and if the order no matter then the total possible pairs are:  

Pairs = 30 / 2 = 15

So then the best answer would be D. 15

We can also find the solution using combinations. We have a total of 6 nooks, and we want to select two so then we hav C(6, 2) ways to select two. We need to remember that the formula for combinatories is given by:

$nCx = C(n,x) = \frac{n!}{x! (n-x)!}$

Where $n! = n * (n-1)!$

And if we replace the values we got this:

$6C2= C(6, 2) = \frac{6!}{2! (6-2)!}=\frac{6!}{2! 4!}=\frac{6*5*4!}{2! 4!}= 15$  

And as we can see we got the same solution from the previous part.