The number of ways in which four different letters can be put in their four addressed envelopes such that atleast two of them are in the wrong envelopes are

Question

The number of ways in which four different letters can be put in their four addressed envelopes such that atleast two of them are in the wrong envelopes are, 23, 25, 6, 7

MARKS App · Accepted Answer

Two in wrong envelops = 4 C 2 × 2 ! 1 2 ! = 6 Three in wrong envelops = 4 C 1 × 3 ! 1 2 ! - 1 3 ! = 4 3 - 1 = 8 Four in wrong envelops = 4 ! 1 2 ! - 1 3 ! + 1 4 ! = 12 - 4 + 1 = 9 The total ways = 6 + 8 + 9 = 23

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