Question Of The Day

There are seven greeting cards, each of a different colour, and seven envelops of the same seven colours. The number of ways in which the cards can be put in the envelopes, so that exactly four of the cards go into the envelopes of the right colours, is

a) ⁷C₃

b) (2)( ⁷C₃)

c) (3!)(⁴C₃)

d)  (3!)( ⁷C₃) (⁴C₃)

Ans: b) (2)( ⁷C₃)

The 3 cards which do not go into the envelopes of the right colours can be chosen in ⁷C₃ way. Now, the 3 cards can go into the wrong envelopes in 2 × 1 × 1 ways. so 2(⁷C₃) ways.