Concept:
C(n,r−1)+C(n,r)=C(n+1,r)
Calculation:
⇒C(47,4)+C(51,3)+C(50,3)+C(49,3)+C(48,3)+C(47,3) ={C(47,4)+C(47,3)}+C(51,3)+C(50,3)+C(49,3)+C(48,3)
As we know that, C (n,r−1)+C(n,r)=C(n+1,r)
⇒{C(47,4)+C(47,3)}+C(51,3)+C(50,3)+C(49,3)+C(48,3) ={C(48,4)+C(48,3)}+C(51,3)+C(50,3)+C(49,3) ⇒{C(48,4)+C(48,3)}+C(51,3)+C(50,3)+C(49,3) ={C(49,4)+C(49,3)}+C(51,3)+C(50,3) ⇒{C(49,4)+C(49,3)}+C(51,3)+C(50,3)={C(50,4)+C(50,3)}+C(51,3)⇒{C(50,4)+C(50,3)}+C(51,3)={C(51,4)+C(51,3)} =C(52,4)
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