JEE Advanced 2014 Mathematics question
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
Answer: (C)
Solution
The number of derangements of 6 objects is . By symmetry, card 1 is equally likely to go into each of the 5 envelopes 2, …, 6 among these derangements, so the
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