EXAMPLE 1.5.15 Classic example of combinations

The Florida Lotto Saturday night drawing used to work like this:

There are 49 ping-pong balls in a machine, each bearing a number from 1 to 49. The machine randomly spits out 6 ping-pong balls. If the numbers on the ping-pong balls match the six numbers that you chose, YOU WIN!

How many different outcomes are possible?

SOLUTION

In order to win this LOTTO you need to pick the same six numbers that the machine produces; you don't need to predict the order in which the machine produces the six numbers. For instance, the outcome 41-2-31-12-9-26 is the same as the outcome 31-41-2-26-12-9; rearranging the six elements does not give a different outcome. For this reason, the number of outcomes is determined by the number of combinations of 49 things taken 6 at a time.

Now, the Lotto works like this: there are 53 balls instead of 49. How many

outcomes are possible under this new scheme?

SOLUTION

In this case the number of solutions is the number of combinations of 53 things taken 6 at a time:

Be sure that you are able to use your calculator correctly in order to arrive at this result!