a player wins first prize by selecting the correct 5-number combination when 5 different numbers from 1 through 59 are drawn. It doesn’t matter what order the numbers are drawn in as long as all 5 numbers match
- How many 5-number combinations are there out of 59 numbers?
- How many 5-number combinations would there be if they were drawn from 60
different numbers (i.e., 1 through 60)?

Question

a player wins first prize by selecting the correct 5-number combination when 5 different numbers from 1 through 59 are drawn.  It doesn’t matter what order the numbers are drawn in as long as all 5 numbers match
- How many 5-number combinations are there out of 59 numbers?
- How many 5-number combinations would there be if they were drawn from 60
different numbers (i.e., 1 through 60)?

anonymous · Answer

4,486,242
combinations of 60 items taken 5 at a time = n!/r!(n-r)! = 60!/5!55!