\( \frac{{ }_{7} P_{7}}{(5!)(3!)}\left(P_{2}{ }^{5}\right) \)
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The formula for permutations is: \[ {}_{n}P_{r} = \frac{n!}{(n-r)!} \] For \( {}_{7}P_{7} \): \[ {}_{7}P_{7} = \frac{7!}{(7-7)!} = \frac{7!}{0!} = 7! \] Since \( 0! = 1 \), we have: \[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 \] Show more…
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