Question

2. If P( 8,r ) = 336, which of the following is the value of r? A 2 B. 3 C. 4 D5​

Answer 1

Answer:

3

Step-by-step explanation:

npr = n!/(n-r)!

8pr = 8!/(8-r)! = 336

if we substitute r = 3

8p3 = 8!/(8-3)! = 8!/5! = 8 ×7×6×5!/5!= 8×7×6 = 336

Answer 2

The value of r = 3

Given :

P( 8,r ) = 336

To find :

The value of r is

A. 2

B. 3

C. 4

D. 5

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

P( 8,r ) = 336

Step 2 of 2 :

Find the value of p

$\displaystyle \sf{ P( 8,r ) = 336 }$

$\displaystyle \sf{ \implies {}^{8}P_r = 336 }$

$\displaystyle \sf{ \implies {}^{8}P_r = 8 \times 7 \times 6 }$

$\displaystyle \sf{ \implies {}^{8}P_r = \frac{(8 \times 7 \times 6) \times (5 \times 4 \times 3 \times 2 \times 1)}{(5 \times 4 \times 3 \times 2 \times 1)} }$

$\displaystyle \sf{ \implies {}^{8}P_r = \frac{8!}{5 !} }$

$\displaystyle \sf{ \implies {}^{8}P_r = \frac{8!}{(8 - 3) !} }$

$\displaystyle \sf{ \implies {}^{8}P_r = {}^{8}P_3 }$

Comparing both sides we get r = 3

Hence the correct option is B. 3

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