#### Parent Mathing Tip #11: Money

These tips give parents ideas for math exercises that will develop their child's math abilities. Today’s parent tip for “mathing” with your child focuses on money.

It's another Word Problem Wednesday! Today's word problem explores probability as it relates to the lottery. Give it a shot—we'll update this article with the answer tomorrow!

For a certain lottery, there are 20 balls numbered 1 to 20. You select 4 numbers. Lottery officials then draw 4 balls without replacement. You win if you match the 4 selected numbers. What is the probability of winning this lottery?

**Update:** Here's the solution!

There are 4 winning numbers to select for the first drawing and 20 numbers to choose from, so the probability that the first number drawn is a winning number is 4/20.

For the second drawing, there are now 3 winning numbers to select for the second drawing and 19 numbers to choose from, so the probability that the second number drawn is a winning number is 3/19.

Continuing this pattern, the probability that the third drawing is a winning number is 2/18, and the probability that the fourth drawing is a winning number is 1/17.

Multiplying these fractions together gets us 4/20 x 3/19 x 2/18 x 1/17 = **1/4,845**.

Alternatively, since order does not matter, this is a combination. From the 20 total balls, we are selecting 4 of them. 20C4 = 20! / [(20 – 4)! x 4!] = 4,845, so there is 4,845 different combinations of drawing 4 balls from 20 total balls. Since there is only 1 winning combination, the probability of selecting the winning combination is 1/4,845.

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