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Probability Problems- Need to know what I'm doing wrong?
I have two probability questions I can't figure out.
1) In a Power Ball lotrry, 5 numbers between 1 and 12 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the numbers is drawn is not important.
My answer: 95040.
How I got there: For the first possible spot, there are 12 possibilities. For the second, only 11. For the third, 10, etc... Comes out to 12*11*10*9*8=95040
Apparently that is wrong. Can you please explain why?
2) If the police have 9 suspects, how many ways can they select 5 for a lineup?
My answer: 15120. Same as above- 9*8*7*6*5=15120
Could the answer be 9^5= 59049?
I don't just want the answers. I want to know what I'm doing wrong. Please, help!
1 Answer
- 9 years agoFavorite Answer
Hi there, your reasoning is very good and you ended up close!
The only thing you're missing is an important concept: that order is NOT important. The questions here are Combinations as opposed to Permutations. Your answers are currently Permutations. With Combinations we don't worry about order, so we divide the answers by a factor of r! Why? because r! tells us the number of ways r (number of samples taken) can be arranged in order. For example, if we were drawing out 3 balls we'd divide by 3! = 3 x 2 x 1 = 6. This result of 6 is the exact number of ways you could order the digits from 1 to 3, so that's why we need to divide by it when order's not important.
1) The number of balls is 5, ie. r = 5
95040 / r!
= 95040 / 5!
= 792
2) r = 5
15120 / r!
= 95040 / 5!
= 126
If you haven't used it before, the '!' key (factorial key) is on your calculator. The more general formula for these types of questions is:
n! / (r! (n - r)!)
A shortcut on your calculator is the 'nCr' button, where 'n' is the sample size (e.g. number of balls) and 'r' is the number you're sampling. For permutations, use the 'nPr' button.
