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Question -

If 15C3r = 15Cr + 3,find r.



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 15C3r = 15Cr + 3,we can say that

Let us check forcondition (i)

3r = r + 3

3r – r = 3

2r = 3

r = 3/2

We know that for acombination nCr, r≥0, r should be a positive integerwhich is not satisfied here,

So, the condition (ii)must be satisfied,

15 = 3r + r + 3

15 – 3 = 4r

4r = 12

r = 12/4

= 3

 The value of ris 3.

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