# Sandwich prob, combinations

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I found a problem, I just like to check it.

Question: From 8 total ingredients, (ham being one)- what's the probability of choosing a sandwich with ham?

My solution:

27/28 = 128/256 = 1/2

Edited by psyclones
typo

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Did I complete the above post incorrectly?

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The question is inderminate because it depends upon the meaning of the phrase 'total ingredients'.

Do you mean 8 sandwich fillings?

If so, is there only one filling that includes ham?

The basic probability, assuming every sandwhich has one filling and there are an equal number of sandwiches with each filling is 1 in 8.

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I've paraphrased the question: Yes it's 8 filling ingredients. I thought too that it was 1/8, but I don't believe that's the answer.  The topic is combination(s) (nCr) within the text. so the sandwich can have ham only, or ham and lettuce, or ham and tomato, or ham tomato and lettuce and so on.. up to 7 other ingredient fillings combined with ham.

Does that help to clarify the problem?  I can't remember how to use Latex code on your site or I'd show my working using nCr notation.

[ nCr(7,0) + nCr(7,1)+nCr(7,2) + ... +nCr(7,6) +nCr(7,7) ]  /  [  nCr(8,0) + nCr(8,1)+nCr(8,2) + ... +nCr(8,7) +nCr(8,8) ] = 2^7 / 2^8

given:   nCr(n,0) + nCr(n,1)+nCr(n,2) + ... +nCr(n, n-1) +nCr(n ,n )  = 2^n

Edited by psyclones
typo

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