Question

Number of ways of selecting $6$ shoes, out of $6$ pair of shoes, having exactly two pairs is

• A. $1440$
• B. $240$
• C. $360$
• D. $720$

Answer 1

The correct option is C $360$

We can select $2$ pairs of shoes from $6$ pairs in ${}^6{C}_2$ ways
Now rest $2$ shoes we can select from $8$ shoes such that no pairs of shoes gets selected
So selection of $2$ shoes can be done in ${}^8{C}_2$ ways but we have to remove the cases in which one pair of shoes gets selected which is ${}^4{C}_1$
$\therefore$ Required number of ways
$={}^6{C}_2\times \left({}^8{C}_2-{}^4{C}_1\right)=360$