Question -
Answer -
We know that if┬аnCp┬а=┬аnCq,then one of the following conditions need to be satisfied:
(i) p = q
(ii) n = p + q
So from thequestion┬аnC10┬а=┬аnC12,we can say that
10 тЙа 12
So, the condition (ii)must be satisfied,
n = 10 + 12
n = 22
Now, we need tofind┬а23Cn,
We know the value of nso,┬а23Cn┬а=┬а23C22
Let us use theformula,
nCr┬а= n!/r!(n тАУ r)!
So now, value of n =23 and r = 22
nCr┬а= n!/r!(n тАУ r)!
23C22┬а= 23! / 22!(23 тАУ 22)!
= 23! / (22! 1!)
= [23├Ч22!] / (22!)
= 23
тИ┤┬аThe valueof┬а23C22┬а= 23.