How do you simplify $\frac{15!}{2! 7!}$ $(15!)/(2!7!)$ ?

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How do you simplify $\frac{15!}{2! 7!}$ $(15!)/(2!7!)$ ?

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Answer 1 · 2016-12-13T17:29:07

We can rewrite as
$15! = 15 \times 14! = 15 \times 14 \times 13! . .$ $15! = 15xx14! = 15xx14xx13! ..$ and so on
So $15 = 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7!$ $15=15xx14xx13xx12xx11xx10xx9xx8xx7!$

And so,
$\frac{15!}{2! 7!} = \frac{15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7!}{2! 7!}$ $(15!)/(2!7!) = (15xx14xx13xx12xx11xx10xx9xx8xx7!)/(2!7!)$
$\ \ \ \ \ \ \ \ = (15xx14xx13xx12xx11xx10xx9xx8)/(2!)$
$\ \ \ \ \ \ \ \ = (15xx14xx13xx12xx11xx10xx9xx8)/(2)$
$\ \ \ \ \ \ \ \ = 129739600$

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How do you simplify $\frac{15!}{2! 7!}$ $(15!)/(2!7!)$ ?

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