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 nC10 = nC12,we can say that
10 ≠ 12
So, the condition (ii)must be satisfied,
n = 10 + 12
n = 22
Now, we need tofind 23Cn,
We know the value of nso, 23Cn = 23C22
Let us use theformula,
nCr = n!/r!(n – r)!
So now, value of n =23 and r = 22
nCr = n!/r!(n – r)!
23C22 = 23! / 22!(23 – 22)!
= 23! / (22! 1!)
= [23×22!] / (22!)
= 23
∴ The valueof 23C22 = 23.