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Six cards and 6 envelopes and number 123456 and the cards are to be placed in annual up so that each envelope contain exactly one card and no card is placed in the angular pairing the same number and moreover the card number one is always placed in envelope number to then number of days it can be done is
Number of derrangements of 6 = 6! (1 – 1/1! + 1/2! - 1/3! + 1/4! – 1/5! + 1/6!)= 360 – 120 + 30 – 6 + 1= 265Out 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.
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