Number of subsets for {7,19,4,20}

Question

Subset for {7,19,4,20}

Answer 1

There is 1 way to grab all four items: {7, 19, 4, 20}

There are 4 ways to grab 3 of the 4 items: {7, 19, 4}, {7, 19, 20}, {7, 4, 20}, {19, 4, 20}

There are 6 ways to grab 2 of the 4 items: {7, 19}, {7, 4}, {7, 20}, {19, 4}, {19, 20}, {4, 20}

There are 4 ways to grab 1 of the 4 items: {7}, {19}, {4}, {20}

There is 1 way to grab 0 of the 4 items: {∅}

 

This means there are 1 + 4 + 6 + 4 + 1 = 16.  Note that 16 is also 2⁴.

 

In general, the total number of subsets in a set with n elements is 2ⁿ.