What is (30!)/(5!(30-5)!) ?

The solution to (30!)/(5!(30-5)!) is 142506

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simplify (30!)/(5!(30-5)!)

simplify

\frac{30 !}{5 ! ( 30 - 5 ) !}

142506

Solution steps

\frac{30 !}{5 ! ( 30 - 5 ) !}

Subtract the numbers:

30 - 5 = 25

= \frac{30 !}{5 ! \cdot 25 !}

Cancel the factorials:

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

\frac{30 !}{25 !} = 30 \cdot 29 \cdot 28 \cdot 27 \cdot 26

= \frac{30 \cdot 29 \cdot 28 \cdot 27 \cdot 26}{5 !}

\frac{30 \cdot 29 \cdot 28 \cdot 27 \cdot 26}{5 !} = 142506

= 142506

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e^{\frac{π}{4} i}