Question

How many subsets are there in {1, 2, 3, 4, 5, 6}?

Answer 1

64

Step-by-step explanation:

For a set with n elements, there are 2n subsets.

In this case, # of subsets =26=64

∅,

{1},{2},{3},{4},{5},{6},

{1,2},{1,3},{1,4},{1,5},{1,6},{2,3},{2,4},{2,5},{2,6},{3,4},{3,5},{3,6},{4,5},{4,6},{5,6},

{1,2,3},{1,2,4},{1,2,5},{1,2,6},{1,3,4},{1,3,5},{1,3,6},{1,4,5},{1,4,6},{1,5,6},{2,3,4},{2,3,5},{2,3,6},{2,4,5},{2,4,6},{2,5,6},{3,4,5},{2,4,6},{3,5,6},{4,5,6},

{1,2,3,4},{1,2,3,5},{1,2,3,6},{1,2,4,5},{1,2,4,6},{1,2,5,6},{1,3,4,5},{1,3,4,6},{1,3,5,6},{1,4,5,6},{2,3,4,5},{2,3,4,6},{2,3,5,6},{2,4,5,6},{3,4,5,6},

{1,2,3,4,5},{1,2,3,4,6},{1,2,3,5,6},{1,2,4,5,6},{1,3,4,5,6},{2,3,4,5,6},

{1,2,3,4,5,6}

Answer 2

Answer: 64

Step-by-step explanation:

If there are n = 6 items in the set, then there are 2^n = 2^6 = 64 subsets

This is because there are 2 choices per slot. Either the item is in the subset or not. Since we have 6 slots, and 2 choices per slot, we have (2*2*2)*(2*2*2) = 2^6 = 64 different combos.

Side note: The empty set is included as one of the subsets. Also, the original set itself is a subset.