If nC10 = nC12, find 23Cn.

Asked by Sakshi | 1 year ago |  30

Solution :-

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 the question nC10 = nC12, we can say that

10 ≠ 12

So, the condition (ii) must be satisfied,

n = 10 + 12

n = 22

Now, we need to find 23Cn,

We know the value of n so, 23Cn = 23C22

Let us use the formula,

nCr =$$\dfrac{ n!}{r!(n – r)!}$$

So now, value of n = 23 and r = 22

nCr = $$\dfrac{ n!}{r!(n – r)!}$$

23C22 = $$\dfrac{23! }{ 22!(23 – 22)!}$$

= 23

The value of 23C22 = 23.

Answered by Sakshi | 1 year ago

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