Math miscellaneousHard
Question
The value of 50C4 + 
56-rC3 is
56-rC3 is Options
A.55C4
B.55C3
C.56C3
D.56C6
Solution
56C4 + 
56-rC3
⇒ 50C4 + [55C3 + 54C3 + 53C3 + 52C3 + 51C3 + 50C3 ]
= (50C4 + 50C3) + 51C3 + 52C3 + 53C3 + 54C3 + 55C3
(51C4 + 51C3) + 52C3 + 53C3 + 54C3 + 55C3
⇒ 55C4 + 55C3 = 56C4.
56-rC3 ⇒ 50C4 + [55C3 + 54C3 + 53C3 + 52C3 + 51C3 + 50C3 ]
= (50C4 + 50C3) + 51C3 + 52C3 + 53C3 + 54C3 + 55C3
(51C4 + 51C3) + 52C3 + 53C3 + 54C3 + 55C3
⇒ 55C4 + 55C3 = 56C4.
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