Combi offer! #4
Probability
Level
3
6 cards and 6 envelopes are numbered 1 , 2 , 3 , 4 , 5 , 6. Cards are to be placed in envelopes such that card number 1 is always placed in envelope number 2 and no card is placed in the envelope bearing same number. Find total number of ways to arrange the cards in envelopes?
265
53
67
264
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1 solution
The number of derangements of 6 distinct items is 265. Of these derangements, 5 1 of them will involve card number 1 being place in envelope number 2.
Thus the solution is 5 1 ∗ 2 6 5 = 5 3 .
You can read about derangements here: link