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Evaluate the expression 50C4 + ∑(r=1 to 6) 56-r C3.
- 55C4
- 55C3
- 56C3
- 56C4
Correct answer: 56C4
Solution
The expression combines a binomial coefficient and a summation of binomial coefficients, which can be simplified using the hockey-stick identity in combinatorics. This identity states that the sum of the form ∑_(r=k)ⁿ (n-r)/(k-1) = (n+1)/(k) applies here, leading to the result of 56C4.
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