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 years students complete the reading assignment than last years students? a. 36 b. 56 c. 216 d. 336

Explanation:

Step1: Calculate number of ways last year

Use combination formula $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 6$ (books last year) and $k=3$ (books to read). So $C(6,3)=\frac{6!}{3!(6 - 3)!}=\frac{6!}{3!3!}=\frac{6\times5\times4}{3\times2\times1}=20$.

Step2: Calculate number of ways this year

Use combination formula with $n = 8$ (books this year) and $k = 3$ (books to read). So $C(8,3)=\frac{8!}{3!(8 - 3)!}=\frac{8!}{3!5!}=\frac{8\times7\times6}{3\times2\times1}=56$.

Step3: Find the difference

Subtract the number of ways last year from this year: $56-20 = 36$.

Answer:

A. 36