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The value of ∑(r=0 to 20) 50−r C6 is equal to:

1. 51C7 + 30C7
2. 50C7 − 30C7
3. 51C7 − 30C7
4. 50C6 − 30C6

Correct answer: 51C7 − 30C7

Solution

The expression ∑(r=0 to 20) 50−r C6 can be interpreted using the hockey-stick identity in combinatorics, which leads to the result of 51C7 minus the contributions from the excluded cases, represented by 30C7.

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