Question

compute the number of ways you can select n elements from n elements for each of the following: a. n = 2, n = 7 b. n = 5, n = 8 c. n = 7, n = 19 (simplify your answer) a. way(s)

Explanation:

Step1: Recall combination formula

The number of ways to select $n$ elements from $N$ elements is given by the combination formula $C(N,n)=\frac{N!}{n!(N - n)!}$.

Step2: Calculate for part a

For $N = 7$ and $n=2$, we have $C(7,2)=\frac{7!}{2!(7 - 2)!}=\frac{7!}{2!5!}=\frac{7\times6\times5!}{2\times1\times5!}=21$.

Step3: Calculate for part b

For $N = 8$ and $n = 5$, we have $C(8,5)=\frac{8!}{5!(8 - 5)!}=\frac{8!}{5!3!}=\frac{8\times7\times6\times5!}{5!\times3\times2\times1}=56$.

Step4: Calculate for part c

For $N = 19$ and $n = 7$, we have $C(19,7)=\frac{19!}{7!(19 - 7)!}=\frac{19!}{7!12!}=\frac{19\times18\times17\times16\times15\times14\times13\times12!}{7\times6\times5\times4\times3\times2\times1\times12!}=50388$.

Answer:

a. 21
b. 56
c. 50388