Question -
Answer -
We know that if nCp = nCq,then one of the following conditions need to be satisfied:
(i) p = q
(ii) n = p + q
So from thequestion nC4 = nC6,we can say that
4 ≠ 6
So, the condition (ii)must be satisfied,
n = 4 + 6
n = 10
Now, we need tofind 12Cn,
We know the value of nso, 12Cn = 12C10
Let us use theformula,
nCr = n!/r!(n – r)!
So now, value of n =12 and r = 10
nCr = n!/r!(n – r)!
12C10 = 12! / 10!(12 – 10)!
= 12! / (10! 2!)
= [12×11×10!] / (10!2!)
= [12×11] / (2)
= 6×11
= 66
∴ The valueof 12C10 = 66.