Question

nC7=nC4 find value of n

Answer 1

here is your answer

n= 7+4

n=11...........

Answer 2

The value of n is 11

Given:  

$_{7}^{n} C=_{4}^{n} C$

To find:

The value of n

Solution:

The question  $_{7}^{n} C=_{4}^{n} C$ is according to the formula of $\stackrel{n}{r} C=\frac{n !}{r !}(n-r) !$, so write the values in the formula, we get$\left(\stackrel{n}{7} C=\frac{n !}{7 !(n-7) !}\right)= \left(\stackrel{n}{4} C=\frac{n !}{4 !(n-4) !}\right)$, now putting the value and find the combination of  

$\frac{n !}{7 !(n-7) !}=\frac{n !}{4 !(n-4) !}$

Dividing both sides by n! we get the following equation below

$\frac{1}{7 !(n-7) !}=\frac{1}{4 !(n-4) !}$, taking cross multiplication we get

$4 !(n-4) !=7 !(n-7) !$, we pull the division of  7! And 4! On one side of the equal we get

$\frac{(n-4) !}{(n-7) !}=\frac{7 !}{4 !} 210 \text { we get }(n-4)(n-5)(n-6)=210$

solving the n equation we get n = 11.

Hence, the value of n is 11