Question

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and the cards are to be placed on envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is

Answer 1

Hello friend,
Number of derrangements of 6 = 6! (1 – 1/1! + 1/2! - 1/3! + 1/4! – 1/5! + 1/6!)
= 360 – 120 + 30 – 6 + 1
= 265
Out of these derrangements, there are five ways in which card numbered 1 is going wrong.
So, when it is going in envelope numbered 2 is 265/5 = 53 ways.

Hope this may help you.....

Asking questions is a sign of intelligency.