My Math Forum How Many Combinations Are There When 190 Balls Are Drawn Into Groups Of 10?

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 June 21st, 2017, 04:20 PM #1 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 580 Thanks: 80 How Many Combinations Are There When 190 Balls Are Drawn Into Groups Of 10? Balls numbered from 1 to 190 are drawn without replacement into 19 groups of 10. The order within a group doesn't matter. Is the amount of combinations 190 C 10 * 180 C 10 * ... 10 C 10 ?
 June 21st, 2017, 07:02 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,690 Thanks: 859 yes maybe written a bit sexier as $\prod \limits_{k=1}^{19} \dbinom{(20-k)10}{10}$
 June 22nd, 2017, 04:54 AM #3 Senior Member     Joined: Feb 2010 Posts: 634 Thanks: 104 Hmm ... I think you might need to divide this by 19! Balls numbered from 1 to 4 are drawn without replacement into 2 groups of 2. The order within a group doesn't matter. I don't believe the answer is 4C2 * 2C2 = 6. (12)(34), (13)(24), (14)(23) are the only ways. I think you need to divide by 2! since the groups could be rearranged.
June 22nd, 2017, 05:34 AM   #4
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Quote:
 Originally Posted by mrtwhs Hmm ... I think you might need to divide this by 19! Balls numbered from 1 to 4 are drawn without replacement into 2 groups of 2. The order within a group doesn't matter. I don't believe the answer is 4C2 * 2C2 = 6. (12)(34), (13)(24), (14)(23) are the only ways. I think you need to divide by 2! since the groups could be rearranged.
I think the question simply wasn't posed clearly enough, since it wasn't clear whether the orders of groups count...

 June 26th, 2017, 06:33 PM #5 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 580 Thanks: 80 The orders of groups matter.

 Tags 190, balls, combinations, drawn, groups

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