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Middle Years

8.04 Factorial notation (Enrichment)

Worksheet
Factorial notation
1

Evaluate the following expressions:

a

5!

b

3!

c

0!

d

\dfrac{7!}{5!}

e

\dfrac{10!}{9!}

f

\dfrac{6!}{8!}

g

\left(7 - 5\right)!

h

\left(11 - 8\right)!

2

Evaluate the following expressions:

a

4! 6!

b

3! 7!

c

\dfrac{7!}{4!}

d

\dfrac{6!}{0!}

e

\dfrac{0!}{9!}

f

4! \times 5

g

5\times 3! \times 4

h

(2 \times 3)!

3

Evaluate the following expressions:

a

\dfrac{11!}{5! 6!}

b

\dfrac{19!}{15! 4!}

c

\dfrac{6!}{4! 4!}

d

\dfrac{6!2!}{8!4!}

4

Express 6! \times 7 as a single factorial in the form x!.

5

Rewrite each of the following as a single factorial expression:

a
6 \times 5!
b
8 \times 6! \times 7
c
\dfrac{9!}{9}
d
\dfrac{11!}{110}
6

Rewrite the following as a single factorial expression: \left(n - 1\right)! n \left(n + 1\right) for some positive whole number n.

7

Express the following without any factorial notation: \dfrac{\left(n + 2\right)!}{\left(n - 2\right)!} for some positive whole number n.

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