What is (15!)/(5!(15-5)!) ?

The solution to (15!)/(5!(15-5)!) is 3003

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simplify (15!)/(5!(15-5)!)

simplify

\frac{15 !}{5 ! ( 15 - 5 ) !}

3003

Solution steps

\frac{15 !}{5 ! ( 15 - 5 ) !}

Subtract the numbers:

15 - 5 = 10

= \frac{15 !}{5 ! \cdot 10 !}

Cancel the factorials:

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

\frac{15 !}{10 !} = 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11

= \frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{5 !}

\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{5 !} = 3003

= 3003

4 x - 28 y + 4

e^{9} = x

\frac{3 x - 1}{2} - \frac{5 x + 4}{3} - \frac{x + 2}{8} = \frac{2 x - 3}{5} - \frac{1}{10}

12 x - 3 = 10 x + 5

e^{1.1}