What is (10!)/(5!(10-5)!) ?

The solution to (10!)/(5!(10-5)!) is 252

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simplify (10!)/(5!(10-5)!)

simplify

\frac{10 !}{5 ! ( 10 - 5 ) !}

252

Solution steps

\frac{10 !}{5 ! ( 10 - 5 ) !}

Subtract the numbers:

10 - 5 = 5

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

Cancel the factorials:

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

\frac{10 !}{5 !} = 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6

= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6}{5 !}

\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6}{5 !} = 252

= 252

x + \frac{1}{2} < \frac{2 + x}{4}

(\frac{x ^{- 3} y ^{5}}{4 ^{- 3}})^{0}

64 x^{2} - 9 y^{2}

x^{2} - 16 x + 64 < 0

\frac{4}{3} + 8