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Question
Verify that 8C4 + 8C3 = 9C4.
Solution
LHS = 8C4 + 8C3
`= (8*7*6*5)/(4*3*2*1) + (8*7*6)/(3*2*1)`
= 7 × 2 × 5 + 8 × 7
= 70 + 56
= 126
RHS = 9C4
`= (9 xx 8 xx 7 xx 6)/(4 xx 3 xx 2 xx 1)`
= 9 × 7 × 2
= 126
∴ LHS = RHS
Hence verified.
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