Vedant
Last Activity: 7 Years ago
Dear student
The formula for ‘n choose k’ is
n!/(n-k)!k!
Therefore we have
n!/(n-8)!8! = n!/(n-12)!12!
(n-8)!8! = (n-12)!12! ….1
Now there are 2 methods to proceed- guess and check and algebraic
I will first present the guess and check method
To make equation 1 true we must try to equate n-8 to 12 and n-12 to 8
Now we have 2 equations n – 8 = 12 and n – 12 = 8 which give us n = 20
Now the algebraic approach
(n – 8)!8! = (n – 12)!12!
(n – 8)! = (n – 12)! x 12 x 11 x 10 x 9
(n – 8)! / (n – 12)! = 12 x 11 x 10 x 9
On replacing n – 8 by p, we get
p! / (p – 4)! = 12 x 11 x 10 x 9
p x (p-1) x (p-2) x (p-3) = 12 x 11 x 10 x 9
Therefore p = 12 and n – 8 = p
n – 8 = 12
Hence n = 20
Regards
Vedant