Question

find the value of n
np5 = 6720?​

Answer 1

Answer:

nP 5=n! /(n-5)!

6720=n! /(n-5)!

6720=n(n-1) (n-2) (n-3) (n-4) (n-5)! /(n-5)!

6720=n(n-1) (n-2) (n-3) (n-4)

8*7*6*5*4=n(n-1) (n-2) (n-3) (n-4)

8(8-1) (8-2) (8-3) (8-4) =n(n-1) (n-2) (n-3) (n-4)

so, n=8

Answer 2

The value of n = 8

Given :

$\displaystyle \sf{ {}^{n}P_5 = 6720 }$

To find :

The value of n

Formula :

$\displaystyle \sf{ {}^{n}P_r = \frac{n!}{(n - r)!} }$

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf{ {}^{n}P_5 = 6720 }$

Step 2 of 2 :

Find the value of n

$\displaystyle \sf{ {}^{n}P_5 = 6720 }$

$\displaystyle \sf{ \implies {}^{n}P_5 = 8 \times 7 \times 6 \times 5 \times 4 }$

$\displaystyle \sf{ \implies {}^{n}P_5 = \frac{8!}{3!} }$

$\displaystyle \sf{ \implies {}^{n}P_5 = \frac{8!}{(8 - 5)!} }$

$\displaystyle \sf{ \implies {}^{n}P_5 = {}^{8}P_5 } \: \: \bigg[ \: \because \:\displaystyle \sf{ {}^{n}P_r = \frac{n!}{(n - r)!} } \: \bigg]$

$\displaystyle \sf{ \implies n = 8}$

Hence the required value of n = 8

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