Question

If np4 = 1680 find n​

Answer 1

Answer:

Step-by-step explanation:

np4=1680

=10x168=10x8x21

=10x8x7x3=5x2x8x7x3

=8x7x6x5=8P4

=np4=8p4

=n=8

Answer 2

$\displaystyle \sf{ If \: \: {}^{n}P_4 = 1680 \: \: then \: \: n = 8 }$

Given :

$\displaystyle \sf{ {}^{n}P_4 = 1680 }$

To find :

The value of n

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

$\displaystyle \sf{ {}^{n}P_4 = 1680 }$

Step 2 of 2 :

Find the value of n

$\displaystyle \sf{ \implies {}^{n}P_4 = 1680 }$

$\displaystyle \sf{ \implies {}^{n}P_4 = 8 \times 7 \times 6 \times 5 }$

$\displaystyle \sf{ \implies {}^{n}P_4 = \frac{8!}{4!} }$

$\displaystyle \sf{ \implies {}^{n}P_4 = \frac{8!}{(8 - 4)!} }$

$\displaystyle \sf{ \implies {}^{n}P_4 = {}^{8}P_4}$

Comparing both sides we get n = 8

Hence the required value of n = 8

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If 7. 5pr = 7pr – 1, then find r.(question based on permutation and combination chapter)

https://brainly.in/question/26877723

2. If nPr = 3024 and nCr = 126 then find n and r.

https://brainly.in/question/29044585