Post man's dilemma
Algebra
Level
2
Six cards are numbered 1, 2, 3, 4, 5, and 6, and so are six envelopes. Each card is put into an envelope such that
- each envelope contains exactly one card;
- no card is placed in the envelope bearing the same number;
- the card numbered 1 is always placed in the envelope numbered 2.
Then the number of ways it can be done is
53
67
264
265
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1 solution
This can be done using the principle of derangements There can be 2 different cases
Case 1: The card 2 goes to envelope 1 Then the other four letters can be deranged ie, D4=9
Case 2: The card 2 does not go to envelope 1 Then all 5 letters can be deranged ie, D5=44
Thus total ways=D4+D5=9+44=53