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Suppose that a weapons inspector must inspect each of five different sites twice, visiting one site per day. The inspector is free to select the order in which to visit these sites, but cannot visit site $\text{X},$ the most suspicious site, on two consecutive days. In how many different orders can the inspector visit these sites?

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Total ways he can visit sites without any restrictions = $\frac{10!}{2!2!2!2!2!}=\frac{10!}{2^{5}}$

Total ways he can visit sites such that he visits X on consecutive days = $\frac{9!}{2!2!2!2!}=\frac{9!}{2^{4}}$

Here in second the case, we have considered ‘XX’ as just one entity, rest everything remains same.

Therefore number of ways he can visit these sites =  $\frac{10!}{2^{5}}-\frac{9!}{2^{4}}=\frac{9!}{4}=90720$ ways

Answer: 90,720 ways

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admin asked May 1, 2020
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How many different terms are there in the expansion of $(x_{1} + x_{2} +\dots + x_{m})^{n}$ after all terms with identical sets of exponents are added?