There are 4 letters and 4 addressed envelopes. find the probability that all the letters are not dispatched in the right envelope.

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Madhur Jain

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4! (1/2! - 1/3! +1/4! ) = 9
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Let the letter be designated as A,B,C,D and corresponding correct envelopes as 1,2,3,4. FOR EACH LETTER THERE ARE 3 CASES AND FOR EACH CASE 3 POSSIBILITIES. A2 B3 C4 D1 B4 C1 D3 B1 C4 D3 A3 B1 C4 D2 B4 C2 D1 B4 C1 D2 A4 B1 C2 D3 B3 C2 D1 B3 C1 D2 TOTAL...
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Let the letter be designated as A,B,C,D and corresponding correct envelopes as 1,2,3,4. FOR EACH LETTER THERE ARE 3 CASES AND FOR EACH CASE 3 POSSIBILITIES. A2 B3 C4 D1 B4 C1 D3 B1 C4 D3 A3 B1 C4 D2 B4 C2 D1 B4 C1 D2 A4 B1 C2 D3 B3 C2 D1 B3 C1 D2 TOTAL NINE CASES Thus probability that none are dispatched in their right envelopes = 9/24 = 3/8 read less
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Mathematics for JEE Mains/Advanced, XI & XII (All Boards)

Derangement Principle
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The simple direct formula for the envelopes problems is 1/e(for wrong distribution) and (1-1/e) (for atleast 1 enveloep being delivered into right cover)
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Question of Dearrangement :)
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AARAV Mathematics Classes

1 - (1/4!)=23/24
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9
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