How do you evaluate 12P7?

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How do you evaluate 12P7?

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Answer 1 · 2017-02-16T07:09:37

$x^{12} P_{7} = 3991680$ $color(white)(x)^12P_7=3991680$

Explanation:

Perhaps you mean $x^{12} P_{7}$ $color(white)(x)^12P_7$ , which means

the number of ways one chooses a sample of $7$ $7$ objects from a set of $12$ $12$ distinct objects, where order does matter and replacements are not allowed .

As $x^{n} P_{r} = \frac{n!}{(n - r)!}$ $color(white)(x)^nP_r=(n!)/((n-r)!)$

and hence $x^{12} P_{7} = \frac{12!}{(12 - 7)!}$ $color(white)(x)^12P_7=(12!)/((12-7)!)$

= $\frac{12!}{5!} = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1}$ $(12!)/(5!)=(12xx11xx10xx9xx8xx7xx6xx5xx4xx3xx2xx1)/(5xx4xx3xx2xx1)$

= $12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 = 3991680$ $12xx11xx10xx9xx8xx7xx6=3991680$

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How do you evaluate 12P7?

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