Hi there.

My name is Noel and I work in Medical Sciences in Sydney Australia. I have been working with my Year 11 boy on probability and have now manufactured a problem which I cannot solve.

The question relates to the following:

I want to take all numbers in a Lotto game from 1 to 45 and ditribute them between 9 boxes each containing 5 numbers. Each number is used only once.

  1. What is the probability that I derive the correct combination of 5 numbers in the draw?

  2. What is the probability if I take a systems game and now distribute 9 numbers into each of 5 boxes? Once again, the numbers are used only once.

  3. Can you explain what formulae are used and how the answer is derived? Is this a distribution or combination problem? Or is it a combination of both distribution and combination?



Hi Noel,

We will look at the 9 box version first. To start you have 45 numbers and you choose 5 of them to put in the first box. You can do this in ways. Once this is done you can choose 5 of the 40 remaining numbers to put in the second box in ways. Thus the number of ways that you can choose 5 numbers for the first box and 5 numbers for the second box is

Continuing in this fashion there are ways to 5 numbers in each of the first 3 boxes and ays to put 5 numbers in each of the 9 boxes. This number can be simplified to which is approximately 2.32 x 1037

Once the 45 numbers have been placed in 9 boxes and the draw is about to take place, there are 9 draws that will result in you winning. Thus the probability that you win is approxinately

Can you now see how to solve your second problem?

Andrei and Penny
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