What is (20!)/(14!(20-14)!) ?

The solution to (20!)/(14!(20-14)!) is 38760

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simplify (20!)/(14!(20-14)!)

simplify

\frac{20 !}{14 ! ( 20 - 14 ) !}

38760

Solution steps

\frac{20 !}{14 ! ( 20 - 14 ) !}

Subtract the numbers:

20 - 14 = 6

= \frac{20 !}{14 ! \cdot 6 !}

Cancel the factorials:

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

\frac{20 !}{14 !} = 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15

= \frac{20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15}{6 !}

\frac{20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15}{6 !} = 38760

= 38760

n

4 x^{2} + 52 x + 160

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3 x - 1 = 4 x - 11

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