Question

Without writing them all out, what is the number of subsets of set A ={king, queen, knight, prince, princess, duke, earl}?
please show work!

Answer 1

U can either include or not each element so 2 choices each time

2*2*2*2*2*2*2 = 2^7

Answer 2

Subset of 7: 1
Subset of 6: 7
Subset of 5: 7*6*5*4*3/5!=21
Subset of 4: 7*6*5*4/4!=35
Subset of 3: 7*6*5/3!=35
Subset of 2: 7*6/2!=21
Subset of 1: 7
So it is 127 if you count the subset with all elements.

Answer 3

u forgot the empty set.