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How many different sandwiches are possible if the restaurant lets you build a sandwich by choosing any 4 out of 10 sandwich ingredients?

a. 210
b. 120
c. 2520
d. 720

User Gratz
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1 Answer

2 votes

Final answer:

Calculating the number of combinations for choosing 4 out of 10 sandwich ingredients, the formula C(10, 4) gives us 210 different possible sandwiches. Thus, the correct answer is (a) 210.

Step-by-step explanation:

The question involves calculating the number of different ways to combine 4 ingredients out of 10 available options to make a sandwich. This is a problem of combinations, where the order doesn't matter, and it can be solved using the combination formula which is C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from, and k is the number of items to choose.

In this case, we have n = 10 sandwich ingredients and we want to choose k = 4 of them. So the calculation would be: C(10, 4) = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10*9*8*7) / (4*3*2*1) =

The calculation simplifies to 210 different possible sandwiches. Therefore, the correct answer is (a) 210.

User Lighthart
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