Question

if np3=720 find n. ​

Answer 1

hey mate your answer is

@Raj Singh......

Answer 2

The value of n = 10

Given :

$\displaystyle \sf{ {}^{n}P_3 = 720 }$

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

$\displaystyle \sf{ {}^{n}P_3 = 720 }$

Step 2 of 2 :

Find the value of n

$\displaystyle \sf{ {}^{n}P_3 = 720 }$

$\displaystyle \sf{ \implies {}^{n}P_3 = 10 \times 9 \times 8 }$

$\displaystyle \sf{ \implies {}^{n}P_3 = \frac{10!}{7!} }$

$\displaystyle \sf{ \implies {}^{n}P_3 = \frac{10!}{(10 - 3)!} }$

$\displaystyle \sf{ \implies {}^{n}P_3 = {}^{10}P_3 } \: \: \bigg[ \: \because \:\displaystyle \sf{ {}^{n}P_r = \frac{n!}{(n - r)!} } \: \bigg]$

$\displaystyle \sf{ \implies n = 10}$

Hence the required value of n = 10

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