Question

There are 8 different pairs of socks. The number of ways of selecting a total of 6 socks such that exactly 2 pairs are taken is

• A. $1320$
• B. $1512$
• C. $1680$
• D. $1720$

Answer 1

The correct option is C $1680$

8 different pair =${8_C}_2$=28

Then choose two pairs from the remaining 66 for which you will (later) make two incomplete pairs, for ${6_C}_2$ =15 choices.

Finally from each of those two incomplete pairs, choose one shoe, for 2*2=422=4 choices.

Total ways =28*15*4=1680