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Need help with this question, my textbook has the solution but I don't know how to get it.

15 coins in a bag. Three 5 rand coins Five 2 rand coins Seven 1 rand coins

What is the prob that if I pull out 5 random coins, it equals 10 rand The solution is 0.1752

I put all possible options that would give 10 rand over 15 choose 5, but unless I missed one which I'm pretty sure I haven't, I got the wrong answer of 0.441

Gavriel Cohen
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  • @saulspatz I have tried but the solution is very long as it has all the possible combination sequences over the sample space so it would be difficult to post and type out – Gavriel Cohen Mar 24 '19 at 15:12
  • You only have to figure out what combinations add up to $10$ rands. There are very few. – saulspatz Mar 24 '19 at 16:05
  • There are 8 that I worked out, but it comes to the wrong answer – Gavriel Cohen Mar 24 '19 at 16:32
  • @saulspatz just wanted to thank you for your help, completely forgot about the condition of only 5 coins being picked - feeling a little embarrassed – Gavriel Cohen Mar 24 '19 at 17:51

1 Answers1

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There are ${15\choose 5}=3003$ ways to pick $5$ coins.

The only ways for them to add up to $10$ rands are if you choose $5$ two-rand coins (one way) or $1$ five-rand coin, $1$ two-rand coin, and $3$ one-rand coins (${3\choose1}{5\choose1}{7\choose3}=525$ ways.) So the probability is $${526\over3003}=0.17515817515817517...$$

saulspatz
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