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Solve the following factorial problems: a) (6!)/(4!2!) b) (7!)/(6!)

April 16, 2026Mathematics

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2 parts

15

7

7 steps

Here are the solutions to the factorial problems:

Solve $\frac{6!}{4!2!}$

Expand the factorials.
$\frac{6!}{4!2!} = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{(4 \times 3 \times 2 \times 1)(2 \times 1)}$
Rewrite $6!$ as $6 \times 5 \times 4!$ to simplify.
$\frac{6 \times 5 \times 4!}{4! \times 2!}$
Cancel out $4!$ and calculate $2!$.
$\frac{6 \times 5}{2 \times 1} = \frac{30}{2}$
Simplify the fraction.
$\frac{30}{2} = 15$
The value is $\boxed{15}$ .

Solve $\frac{7!}{6!}$

Expand the factorials.
$\frac{7!}{6!} = \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1}$
Rewrite $7!$ as $7 \times 6!$ to simplify.
$\frac{7 \times 6!}{6!}$
Cancel out $6!$.
$7$
The value is $\boxed{7}$ .

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