What is (9!)/((9-3)!*3!) ?

The solution to (9!)/((9-3)!*3!) is 84

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simplify (9!)/((9-3)!*3!)

simplify

\frac{9 !}{( 9 - 3 ) ! \cdot 3 !}

84

Solution steps

\frac{9 !}{( 9 - 3 ) ! \cdot 3 !}

Subtract the numbers:

9 - 3 = 6

= \frac{9 !}{6 ! \cdot 3 !}

Cancel the factorials:

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

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

= \frac{9 \cdot 8 \cdot 7}{3 !}

\frac{9 \cdot 8 \cdot 7}{3 !} = 84

= 84

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ln ∣ 4 ∣

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