I am a secondary student and I was wondering if there was a better way to find out how many combinations and what they are in the lotto 6/49 than writing them out on a piece of paper. Any help you can provide me with would be greatly appreciated.

The number of them is 49 'choose' 6, 49C6, where nCr = n!/[r!(n-r)!] and where m factorial is given by m! = m(m-1)(m-2)...(3)(2)1. If you work this out you will see that there are nearly 14 million different combinations, the exact value is 13,983,816. You could spend a good part of your life trying to write them all out! This topic of permutations and combinations is normally covered in the secondary curriculum. You might like to look at Thoughts on teaching Permutations, Combinations and the Binomial Theorem, a note I wrote some time ago.

Penny