Find The Number Of Subsets The Set Has. {1,2,3,4,5,6,7,8,9}. 511,9,256,512, Can You Help?

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Anonymous Profile
Anonymous answered
The total number of subsets of any n-element set is 2^n. 2^9=512
linda butch Profile
linda butch answered
The correct answer is (D)  512
Anonymous Profile
Anonymous answered
Find the number of subsets of {4, 5, 6}
Oddman Profile
Oddman answered
There are 510 proper subsets, 511 if you also count the whole set, 512 if you count the empty set, too. They can be counted as follows.

1 subset consisting of the entire set
9 subsets consisting of 8 elements
36 = 9*8/2 subsets consisting of 7 elements
84 = 9*8*7/(3*2) subsets consisting of 6 elements
126 = 9*8*7*6/(4*3*2) subsets consisting of 5 elements
126 = 9*8*7*6*5/(5*4*3*2) subsets consisting of 4 elements
84 = 9*8*7*6*5*4/(6*5*4*3*2) subsets consisting of 3 elements
36 = 9*8*7*6*5*4*3/(7*6*5*4*3*2) subsets consisting of 2 elements
9 subsets consisting of 1 element

The total is 1 + 2(9+36+84+126) = 511.

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