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 Advanced 2014 · Paper 2
MathematicsSingle correct+3 / -1Question 48 of 60
JEE Advanced 2014 · Paper 2, Mathematics question 48
Answer and worked solution
Official answer: C
After placing card 1 in envelope 2, cards 2-6 go into envelopes 1, 3, 4, 5, 6. Cards 3-6 must avoid their own envelopes; card 2 has no restriction (its envelope is taken).
Split on card 2.
- Card 2 in envelope 1: cards 3-6 are deranged in envelopes 3-6: .
- Card 2 not in envelope 1: treat envelope 1 as card 2's forbidden "own" envelope. Then all five cards are deranged: .
Total. .
(C)
Topics:Derangements