A person writes letter to six friends and addresses the corresponding envelopes. Let x be the numbers of ways so that at least two of the letters are in wrong envelopes and y be the numbers of ways so that all the

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Quantrex Academy · Accepted Answer

Correct answer: C. 454

Since only one letters can not be in wrong envelope so that at least two letters are in wrong envelope means all the letters are not in right envelopes.

$∴ x = 6 ! - 1 = 720 - 1 = 719$

$Y =$ number of ways, so that all the letters are in wrong envelops

$= 6 ! \left(1 - \dfrac{1}{1 !} + \dfrac{1}{2 !} - \dfrac{1}{3 !} + \dfrac{1}{4 !} - \dfrac{1}{5 !} + \dfrac{1}{6 !}\right)$

$= 360 - 120 + 30 - 6 + 1 = 265$

$∴ x - y = 719 - 265 = 454$

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