if ¹⁵C_3r = ¹⁵C_{r+ 3}, find the value of r

Solution (By Examveda Team)

15 is a superscript of C and 3r, r+3 are subscripts of C. If ¹⁵C_3r = ¹⁵C_{r+ 3} , then we follow the formula:

ⁿC_x = ⁿC_y where x = y OR x + y = n.

Let n represent 15, x = 3r and y = r +3:
3r = r + 3 and 3r + r + 3 = 15
3r = r + 3 ---> 3r - r =3 then 2r = 3 which is r = 3/2
3r + r + 3 = 15 ---> 4r = 12 which is r = 3

r cannot be a fraction since this will give us 1.5 therefore the answer will be r = 3.