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  4. Suman writes letters to his five friends. The number of ways can be letters be placed in the envelopes so that at least two of them are in the wrong envelopes are

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Q. Suman writes letters to his five friends. The number of ways can be letters be placed in the envelopes so that at least two of them are in the wrong envelopes are

Permutations and Combinations

Solution:

$\text { Number of ways }={ }^5 C _2 D _2+{ }^5 C _3 D _3+{ }^5 C _4 D _4+{ }^5 C _5 D _5=10(1)+10(2)+5(9)+1(44)$
$=10+20+45+44=119 $