14!/(3!*11!) — step-by-step solution

Let's calculate:

\frac{14!}{3! \times 11!}

ⓘ For integers n ≥ m ≥ 0, n! = n·(n−1)⋯(m+1)·m!; cancel the common factor m!, which is never zero:

\frac{14!}{3! \times 11!}

\frac{14 \times 13 \times 12}{3!}

\frac{14 \times 13 \times 12}{3!}

ⓘ The factorial of a number is the product of all the integers from 1 to that number:

3!

6

ⅰ

14 \times 13

14 \times (10 + 3)

14 \times 10 + 14 \times 3

140 + 42

182

\frac{182 \times 12}{6}

ⅰ

182 \times 12

182 \times (10 + 2)

182 \times 10 + 182 \times 2

1820 + 364

2184

\frac{2184}{6}

We simplify the fraction:

\frac{2184}{6}

by the common factor:

6

to get the new expression:

364

▶Result:

364