Find r if C(8, r) – C(7, 3) = C(7, 2)
C(8,r) - C(7,3) = C(7,2)
C(8,r) = C(7,2) + C(7,3)
c(8,r) = ((7*6)/(1*2)) + ((7*6*5)/(1*2*3)) [evaluating C(7,2) and C(7,3)]
C(8,r)=21+35
C(8,r)=56
Using the shortcut and hit and try method (not recommended for exams and class work)
(8*7*6)/(1*2*3)=8*7=56
56=56 LHS=RHS
Therefore the value of r =3
C(8,r) = C(7,2) + C(7,3)
c(8,r) = ((7*6)/(1*2)) + ((7*6*5)/(1*2*3)) [evaluating C(7,2) and C(7,3)]
C(8,r)=21+35
C(8,r)=56
Using the shortcut and hit and try method (not recommended for exams and class work)
(8*7*6)/(1*2*3)=8*7=56
56=56 LHS=RHS
Therefore the value of r =3