Question

There are 7 greetings cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective colour is,

• A. $^{7}C_{3}$
• B. $2.^{7}C_{3}$
• C. $3! ^{4}C_{4}$
• D. $3! ^{7}C_{3} \, ^{4}C_{3}$

Answer 1

Answer: (B)

$2.^{7}C_{3}$

Answer 2

$^{7}C_{4} \times 3!\left(\frac{1}{2!}-\frac{1}{3!}\right) = ^{7}C_{3} \times 2$