Question

Select the correct answer.

Every year, Mrs. Hernandez gives her students a summer reading assignment. Last year, she gave her students a list of 6 books and asked them to read any 3. This year, Mrs. Hernandez increased the list to 8 books and asked her students to choose 3. How many more ways can this year’s students complete the reading assignment than last year’s students?

A.
36
B.
56
C.
216
D.
336

Answer 1

A

Explanation:

Plato

Answer 2

A. 36

Explanation:

The order in which the books are chosen is not important. So the combinations formula is used to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

Last year:

3 books from a set of 6. So

`C_(6,3) = (6!)/(3!(6-3)!) = 20`

This year:

3 books from a set of 8. So

`C_(8,3) = (8!)/(3!(8-3)!) = 56`

Difference:

56 - 20 = 36

So the correct answer is:

A. 36