Respuesta :

Answer:

336

Step-by-step explanation:

Using the definition of n[tex]P_{r}[/tex] = n ! / (n- r) !

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

8[tex]P_{3}[/tex]

= 8 ! / (8 - 3) !

= 8 ! / 5 !

= [tex]\frac{8(7)(6)(5)(4)(3)(2)(1)}{5(4)(3)(2)(1)}[/tex]

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

= 8 × 7 × 6 = 336

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ANSWER

[tex]^8P_3 = 336[/tex]

EXPLANATION

Recall that;

[tex]^nP_r = \frac{n!}{(n - r)!} [/tex]

The given expression is:

[tex]^8P_3[/tex]

We substitute n=8 and r=3

[tex]^8P_3 =\frac{8!}{(8- 3)!} [/tex]

[tex]^8P_3 =\frac{8!}{(5)!} [/tex]

This simplifies to :

[tex]^8P_3 =\frac{8 \times 7 \times 6 \times 5!}{5!} [/tex]

We cancel out the common factors to get:

[tex]^8P_3 = 8 \times 7 \times 6[/tex]

[tex]^8P_3 = 336[/tex]

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