To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 55 numbers (one through 55). The order in which the selections is made does not matter. How many different selections are possible.

I believe this problem uses nCr or nPr on the calculator but it may be one factor raised to the power of the other factor... help is appreciated

You're very right; the problem uses nCr as the order does not matter. If done on a calculator it would be calculated by typing 55C6. If calculating manually, we can use the formula for nCr which is: nCr=n!/(r!(n-r)!).

Therefore, the answer to your question would be 55C6=55!/(6!49!)=28989675, quite a lot of combinations!

May 13th, 2015

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