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How many 3 element subsets are there in the set {a,b,c,d,e,f,g}a.7b.140c.70d.21e.35

Question

How many 3 element subsets are there in the set {a,b,c,d,e,f,g}a.7b.140c.70d.21e.35

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Solution

The number of 3-element subsets in a set can be calculated using the combination formula, which is nCr = n! / [(n-r)! * r!], where n is the total number of elements in the set, r is the number of elements in each subset, and "!" denotes factorial.

In this case, the set {a,b,c,d,e,f,g} has 7 elements (n=7), and we want to find the number of 3-element subsets (r=3).

So, we plug these values into the combination formula:

7C3 = 7! / [(7-3)! * 3!] = 7! / [4! * 3!] = (765) / (321) = 35

So, there are 35 3-element subsets in the set {a,b,c,d,e,f,g}. Therefore, the correct answer is e.35.

This problem has been solved

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