Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

If I choose 7 golfers out of 130, and all golfers in the field have an equal chance of winning, how do I work out the probability of at least 1 golfer from my chosen 7 finishing in the top 6?

share|improve this question

2 Answers 2

up vote 3 down vote accepted

Sorting the golfers from the winner to the loser (after the game), there are $\binom {130} 7$ ways to choose the golfers in general, and $\binom {124} 7$ ways to choose the golfers in a way that none of them end up in the top 6. So, the answer is

$$1 - \frac {\binom {124} 7} {\binom {130} 7}$$

share|improve this answer
    
Thanks for the help! –  jonathan innes Mar 20 '13 at 17:59

Hint: The chance that none of your golfers winning is $\frac {123}{130}$. Given that none of yours win, the chance that none finish second is $\frac {122}{129}$. Keep going and multiply to get the chance than none are in the top six. Then subtract from $1$ for the chance that at least one is in the top six.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.