Question

Adrienne has free passes to a music concert and can take $2$ friends along, but she has $5$ friends who could go with her. In how many ways can she select $2$ friends out of $5$?

• A. $10$
• B. $20$
• C. $30$
• D. $15$

Answer 1

The correct option is A $10$

Given that: $n=5$
$r=2$

So, total number of ways
$={}^8{C}_2$
$=\frac{5!}{(5-2)!\times 2!}$
$=\frac{5!}{3!\times 2!}$
$=\frac{5\times 4\times 3!}{3!\times 2\times 1}$
$=5\times 2$
$=10$

Short cut Method to get ${}^5{C}_2$
${}^8{C}_2=\frac{5\times 4}{2\times 1}$
$=10$

Answer:

Total number of ways is $10$.