Let's say you have 5 successes in 7 trials. There are a total of 21 different ways to arrange them. How many times will the longest streak of successes be 5, 4, 3, and 2? I figured this out by brute force, but wondered if there was a formula to calculate it, one that could be used for any x successes in y trials. The answers for the example are:(adsbygoogle = window.adsbygoogle || []).push({});

5 in a row: 3

4 in a row: 6

3 in a row: 9

2 in a row: 3

Thanks for any help.

Ken

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# Longest streaks of successes

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