How do you evaluate the following expression $^{10} P_{6}$ $""^(10)P_(6)$ ?

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Answer 1 · 2017-06-04T08:22:15

$151, 200$ $151,200$

The formula for evaluating a permutation $^{n} P_{r}$ $""^(n) P _(r)$ is $\frac{n!}{(n - r)!}$ $frac(n!)((n - r)!)$ :

$\Rightarrow^{10} P_{6} = \frac{10!}{(10 - 6)!}$ $Rightarrow ""^(10) P _(6) = frac(10!)((10 - 6)!)$

$\Rightarrow^{10} P_{6} = \frac{10!}{4!}$ $Rightarrow ""^(10) P _(6) = frac(10!)(4!)$

$\Rightarrow^{10} P_{6} = 10 \times 9 \times 8 \times 7 \times 6 \times 5$ $Rightarrow ""^(10) P _(6) = 10 times 9 times 8 times 7 times 6 times 5$

$\Rightarrow^{10} P_{6} = 90 \times 56 \times 30$ $Rightarrow ""^(10) P _(6) = 90 times 56 times 30$

$\Rightarrow^{10} P_{6} = 90 \times 1680$ $Rightarrow ""^(10) P _(6) = 90 times 1680$

$therefore ""^(10) P _(6) = 151,200$

How do you evaluate the following expression ""^(10)P_(6)10P6""^(10)P_(6)?