Seven cards and seven envelopes are numbered 1, 2, 3, 4, 5, 6, 7 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 number 1 is always placed in envelope number 2 and 2 is always placed in envelope numbered 3, then the number of ways it can be done is
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If 3 goes in 1 then it is dearrangement of 4 things which can be done in 9 ways.
And if 3 does not goes in 1 then it is dearrangement of 5 things which can be done in 44 ways
total ways = 9 + 44 = 53
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