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Probability and Combinations

Determine the probabilities of events when arrangement order does not matter

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Chance in Lottery Games


Chance in Lottery Games


  • Combination
  • Permutation
  • Probability

Student Exploration

What are your chances of winning the lottery?

The California Fantasy 5 game is a state lottery game played across the state. Anyone eighteen-years-old or older can buy a ticket at a local convenience store. All you have to do is pick five lucky numbers from 1 to 39 on a Fantasy 5 slip. Then every day at 6:30pm entries are closed and the state draws the five Fantasy 5 numbers for the day. Read more about the pickings at http://www.calottery.com/play/draw-games/fantasy-5. Now for the winnings! You win if you get one of the four following outcomes. You pick 2 of the 5 winning numbers, you pick 3 of the 5 winning numbers, you pick 4 of the 5 winning numbers, and you pick 5 of the 5 winning numbers.
What is the probability of picking 5 of the 5 winning numbers?

Extension Investigation

a. Why does this situation represent a Combination?
b. How many different ways can all five of the Fantasy 5 numbers be picked?
c. How many different ways can four of the five Fantasy 5 numbers be picked?
d. If you were analyzing how many ways that two of the five numbers could be picked, how would you approach solving this problem differently?
e. If you were asked to find the probability of picking four of the five Fantasy 5 numbers correctly, how would you approach that task?
f. What would need to change in the problem in order for it to represent a Permutation?

Resources Cited


Connections to other CK-12 Subject Areas

  • Permutations Problems
  • Permutations and Combinations Compared
  • Theoretical and Experimental Probability

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