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┬а15C3r┬а=┬а15Cr + 3,we can say that
Let us check forcondition (i)
3r = r + 3
3r тАУ r = 3
2r = 3
r = 3/2
We know that for acombination┬аnCr, rтЙе0, r should be a positive integerwhich is not satisfied here,
So, the condition (ii)must be satisfied,
15 = 3r + r + 3
15 тАУ 3 = 4r
4r = 12
r = 12/4
= 3
тИ┤┬аThe value of ris 3.