Probability question and the word at least
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Probability question and the word at least

[From: ] [author: ] [Date: 11-05-24] [Hit: ]
I KNOW HOW TO DO IT with the adding method. But that eats up time on a test so i need to know a quicker way to do it. My teacher says when doing at least, you do TOTAL - what is not included in at least (so in this case, 3 and below). but I dont understand what the total is.......
I know when there is at least you could add up it and all the combinations above it, but my teacher said there was a shortcut.
Here is the question:
An icecream vendor sells 15 flavors of icecream. You want to sample AT LEAST 4 of the flavors. How many different combos of ice cream flavors can you sample?
I KNOW HOW TO DO IT with the adding method. But that eats up time on a test so i need to know a quicker way to do it. My teacher says when doing at least, you do TOTAL - what is not included in at least (so in this case, 3 and below). but I don't understand what the total is...
PLEASE explain!!!!! 10 pts most detailed explanation!

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Your teacher's question is 'How many?'. And so, it is not a probability question. It is a question on combinations.
Your answer, perhaps, is 15c4 + 15c5 + 15c6 + .......+15c15 = 32192.


The total number of all possible combinations of 15 objects is 2^15 = 32768.
And so,
(Combinations with four or more) = (total) - (combinations with less than four)
= 2^15 - (15c0 +15c1 +15c2 + 15c3) = 32768 - 576 = 32192

Hope this works.
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