What is (16!)/(4!(16-4)!) ?

The solution to (16!)/(4!(16-4)!) is 1820

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simplify (16!)/(4!(16-4)!)

simplify

\frac{16 !}{4 ! ( 16 - 4 ) !}

1820

Solution steps

\frac{16 !}{4 ! ( 16 - 4 ) !}

Subtract the numbers:

16 - 4 = 12

= \frac{16 !}{4 ! \cdot 12 !}

Cancel the factorials:

\frac{n !}{( n - m ) !} = n \cdot (n - 1) \dots (n - m + 1), n > m

\frac{16 !}{12 !} = 16 \cdot 15 \cdot 14 \cdot 13

= \frac{16 \cdot 15 \cdot 14 \cdot 13}{4 !}

\frac{16 \cdot 15 \cdot 14 \cdot 13}{4 !} = 1820

= 1820

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