Question

Simplify the expression. 8P3

Answer 1

Answer:

336

Step-by-step 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 !

= $\frac{8(7)(6)(5)(4)(3)(2)(1)}{5(4)(3)(2)(1)}$

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

= 8 × 7 × 6 = 336

Answer 2

ANSWER

$^8P_3 = 336$

EXPLANATION

Recall that;

$^nP_r = \frac{n!}{(n - r)!}$

The given expression is:

$^8P_3$

We substitute n=8 and r=3

$^8P_3 =\frac{8!}{(8- 3)!}$

$^8P_3 =\frac{8!}{(5)!}$

This simplifies to :

$^8P_3 =\frac{8 \times 7 \times 6 \times 5!}{5!}$

We cancel out the common factors to get:

$^8P_3 = 8 \times 7 \times 6$

$^8P_3 = 336$