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.
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
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