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

D. 15

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) = (n!)/(x! (n-x)!)`

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

And if we replace the values we got this:

`6C2= C(6, 2) = (6!)/(2! (6-2)!)=(6!)/(2! 4!)=(6*5*4!)/(2! 4!)= 15`

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