Question

if nc5 = nc7 . find the vale of n

Answer 1

Please see the attachment

Answer 2

Answer:

n = 12

Step-by-step explanation:

As given in question,

     $^nC_5\ =\ ^nC_7$

$=>\ \dfrac{n!}{(n-5)!\times 5!}\ = \ \dfrac{n!}{(n-7)!\times 7!}$

$=>\ \dfrac{1}{(n-5)!\times 5!}\ = \ \dfrac{1}{(n-7)!\times 7!}$

$=>\ (n-5)!\times 5!\ =\ (n-7)!\times 7!$

$=>\ (n-5)(n-6)(n-7)!\times 5!\ =\ (n-7)!\times 7\times 6\times 5!$

$=>\ (n-5)(n-6)\ =\ 42$

$=>\ n^2\ -\ 5n\ -\ 6n\ +\ 30\ =\ 42$

$=>\ n^2\ -\ 11n\ -\ 12\ =\ 0$

$=>\ n^2\ -\ 12n\ +\ n\ -\ 12\ =\ 0$

$=>\ n(n-12)\ +\ 1(n-12)\ =\ 0$

$=>\ (n+1)(n-12)\ =\ 0$

$=>\ n\ =\ -1\ or\ 12$

So, the value of n will 12.