Question

Simplify the expression. 8P3

Answer 1

336

Explanation:

Using the definition of n
`P_(r)` = n ! / (n- r) !

where n ! = n(n - 1)(n - 2).... × 3 × 2 × 1

8
`P_(3)`

= 8 ! / (8 - 3) !

= 8 ! / 5 !

=
`(8(7)(6)(5)(4)(3)(2)(1))/(5(4)(3)(2)(1))`

[ cancel 5(4)(3)(2)(1) on numerator/denominator

= 8 × 7 × 6 = 336

Answer 2

`^8P_3 = 336`

EXPLANATION

Recall that;

`^nP_r = (n!)/((n - r)!)`

The given expression is:

`^8P_3`

We substitute n=8 and r=3

`^8P_3 =(8!)/((8- 3)!)`

`^8P_3 =(8!)/((5)!)`

This simplifies to :

`^8P_3 =(8 * 7 * 6 * 5!)/(5!)`

We cancel out the common factors to get:

`^8P_3 = 8 * 7 * 6`

`^8P_3 = 336`