Question

A cow has $8$ different pairs of roller blades. In how many ways can she select $2$ pairs to go skating with her friends?

• A. $24$
• B. $28$
• C. $32$
• D. $36$

Answer 1

The correct option is B $28$

Given that: $n=8$
$r=2$
So, total number of ways
$={}^8{C}_2$
$=\frac{8!}{(8-2)!\times 2!}$
$=\frac{8!}{6!\times 2!}$
$=\frac{8\times 7\times 6!}{6!\times 2\times 1}$
$=4\times 7$
$=28$

Short cut Method to get ${}^8{C}_2$
${}^8{C}_2=\frac{8\times 7}{2\times 1}$
$=28$

Answer:

Total number of ways is $28$.