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

The total number of subsets of any n-element set is 2^n. 2^9=512

{1,2,3,4,5,6,7,8,9,10,11,12}

The correct answer is (D)  512

512

Find the number of subsets of {4, 5, 6}

512

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.

How many subsets does set A have if the set A has 3 elements?

34353454