Question

find n if, n/8!= 3/6! + 1!/4!​

Answer 1

Step-by-step explanation:

n/(8*7*6*5*4!) = 3/(6*5*4!) + 1/4!

1/4! is taken out as common and cancelled

n/(8*7*6*5)=3/(6*5) + 1

n/1680 = 1/10 + 1

n/1680 = 11/10

n=168*11

n=1848

Answer 2

Given:

• $\frac{n}{8!} = \frac{3}{6!} + \frac{1!}{4!}$

To Find:

• The value of 'n'.

Solution:

• Consider the equation, $\frac{n}{8!} = \frac{3}{6!} + \frac{1!}{4!}$  
• ⇒ $\frac{n}{8!} = \frac{3}{6*5*4!} + \frac{1!}{4!}$
• Taking 1/4! as common from the above equation we get,
• ⇒ $\frac{n}{8!} = \frac{1}{4!}[\frac{3}{30}+1]$   (Further simplifying)
• ⇒ $\frac{n}{8!} = \frac{1}{4!}[\frac{1}{10}+1]$  ( solve by taking LCM)
• ⇒ $\frac{n}{8!} = \frac{1}{4!}[\frac{11}{10}]$  
• Re-arranging the above equation to find the value of 'n'.
• ⇒ n = $\frac{8!}{4!}*[\frac{11}{10}]$
• ⇒ n = $\frac{8*7*6*5*4!}{4!}*\frac{11}{10}$
• After cancellation of few terms in the above equation we get,
• ⇒ n = 4*7*6*11
• ⇒ n = 1848

∴ The value of 'n' is 1848.