Special case of Derangement!
Level
1
- Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in 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 !!
- JEE ADVANCE (2014)
67
265
53
264
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1 solution
Number of derangement's 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 derangement's, there are five ways in w which card numbered 1 is going wrong. So, when it is going in envelope numbered 2 is 265/5 = 53 ways. - credit @Yashvardhan Pattanashetti