Question

Find the number of permutations of the first 8 letters of the alphabet taking 2 letters at a time.

Answer 1

\(\dfrac{n!}{(n - r)!}\)

\(\dfrac{8!}{(8 - 3)!}\)

Simplify, what's 8 - 3?

Answer 2

5

Answer 3

336?

Answer 4

Yes, so we have:

\(\dfrac{8!}{5!}\)

Note, the exclamation points mean to multiply all the numbers below it.

For example, 4! is equal to 4 * 3 * 2 * 1

Expand both 8! and 5!:

\(\dfrac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1}\)

\(\dfrac{8 \times 7 \times 6 \times \cancel{5 \times 4 \times 3 \times 2 \times 1}}{\cancel{5 \times 4 \times 3 \times 2 \times 1}}\)

We're left with:

\( 8 \times 7 \times 6\)

Multiply:

\(336\)

You're correct!