Verified answer

Given that elements {8,9,10} are elements of the subset, then the elements

1 through 7 can either be in or out of a subset, i.e., 2 choices for each of the 7

remaining elements. Thus there are 2^7 = 128 subsets of {1,2,...,10} that contain

the set {8,9,10} as a subset.

Basically you are just finding the number of subsets of {1,2,....,7} and then adding

on {8,9,10} at the end.

If you find the number of the subsets of {1,2,3,4,5,6,7} and then add 8,9 and 10 to each, you'll have the subsets of the original set containing 8,9 and 10 , right? So the answer would be the number of the subsets of { 1,2,3,4,5,6,7} which is 2^7=128

:)

It is a logical question.

You are counting sub sets which contains {8,9,10}.

Means you have to think about all the possible combinations from 1 to 7.

Possible combination will be 7! = 1x2x3x4x5x6x7

and last subset is {8,9,10}

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Or

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Formula-use combination

nCr = n!(n-r)!/r!

Yes, how many subsets of {1,2,3,4,5,6,7} are there? 2^7