Alex C.

asked • 07/20/17

help me solve this

You are ordering a hamburger and can get up to 8 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 4 toppings

Kenneth S.

Nobody orders hamburgers this way. Eight toppings would make the darned thing so tall and slippery that it would disintegrate into a slimy mess when lifted toward the mouth.
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07/20/17

Andy C.

lol Kenneth.... too funny
 
The way the question is worded, it asks "What is the probability of getting four toppings."
Not how many ways to select four toppings out of 8.
 
Please clarify the question. Also clarify if toppings are required, or can you get the burger plain?
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07/21/17

Kenneth S.

My answer below is based on inclusion of plain (0 toppings) but it gives different weights (probabilities) because there are so many ways to get n toppings. If the burger maker does things randomly, each different, there are many ways to have 4 toppings--distinct combinations--and I wanted to reflect that weighting. This seems to me to be the most likely interpretation. But I will agree that the question is a strange one, and it is not entirely clear if the probabilities of n toppings are all equal, for all possible numbers (n) of toppings.
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07/21/17

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Kenneth S. answered • 07/20/17

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You might get 0 toppings, or 1, or 2, or ...or 7 or 8..
 
4 toppings can be done by choosing any combination of four of the 8 possible toppings; 8C4 =70 ways!
 
All possible combinations (# of them) is the sum of all terms of the form
 
8Cr where r goes from 0 to 8, and this happens to equal (1+1)^8 which equals 256.
 
Therefore the answer is 70/256, or 0.2734approx.
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Andy C. answered • 07/20/17

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Well naively, there are 9 possibilities.
 
The first possibility is that the cashier can surprise you with a totally empty hamburger with no toppings at all.
Then you have the other 8.
 
So the probability the cashier will select any four toppings is 1/9.
 
 
 
 
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Kenneth S.

Andy, I disagree.  Please see my answer.  It uses the binomial theorem!
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07/20/17

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