Lottery Word Problem

Question

When the jackpot in a lottery gets very high, more people buy tickets. After all, someones going to win right? Suppose there are 49 numbers to choose 6 from. The order doesnt matter in which the numbers are selected. How many possible 6-number lottery tickets are possible if you must also select the powerball from a different set of 10 numbers?

Answer 1

I like to use an acronym I learned form a High School Student, CONI POI

 

Combination

Order

Not

Important

 

Permutation

Order

Important

 

Now they tell us right away that order doesn't mater, so we automatically know we are going to use a Combination.

 

so it is ₄₉C₆, or 49 Choose 6.  Most calculators have Combinations and Permutations readily available but I'll say yours does not so lets get the formula for Combinations:

 

_nC_r = n! ÷ r!(n-r)!

 

the ! means factorial.  In our case, n=49 and r=6, so lets put those in the formula

 

₄₉C₆ = 49! ÷ 6!(49-6)! = 49! ÷ (6!*43!)

 

That value you can put into your calculator and get the answer for the first 6 numbers chosen.  

 

13,983,816 possible tickets.

 

Once we have that, then we must consider the powerball from another set of 10 numbers.  Now think about it this way, if you have 2 pairs of pants and 10 shirts, you can wear each shirt with 10 different pants and have a different outfit.  Since you have 2 shirts, you have 10 outfits for each shirt, so in total 20 outfits, or 2 times 10.

 

So once we figure out the number of possible tickets for the first 6 numbers, we simply multiply that by the powerball options, 10, and we will arrive at our answer.

 

139,838,160