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The number of ways in which four letters can be put in four addressed envelops so that no letter goes into envelope meant for it is
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Verified Answer
The correct answer is:
9
Let $n=4$ be number of envelopes in which number letters goes into envelope meant for it. Then, the number of ways $=4 !-\sum_{k=1}^4{ }^4 C_k$
$$
\begin{aligned}
& {\left[\because \text { required number of ways }=n !-\sum_{k=1}^n{ }^n C_k\right] } \\
= & 24-\left[{ }^4 C_1+{ }^4 C_2+{ }^4 C_3+{ }^4 C_4\right] \\
= & 24-[4+6+4+1]=24-15=9
\end{aligned}
$$
Hence, required number of ways $=9$
$$
\begin{aligned}
& {\left[\because \text { required number of ways }=n !-\sum_{k=1}^n{ }^n C_k\right] } \\
= & 24-\left[{ }^4 C_1+{ }^4 C_2+{ }^4 C_3+{ }^4 C_4\right] \\
= & 24-[4+6+4+1]=24-15=9
\end{aligned}
$$
Hence, required number of ways $=9$
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