you pick a card, roll a die, and find the sum. how many different sums are possible?

Explanation:

Step1: List all possible combinations

Pick card 5 and roll die values from 1 - 6: sums are 5 + 1=6, 5 + 2 = 7, 5+3 = 8, 5 + 4=9, 5+5 = 10, 5+6 = 11. Pick card 6 and roll die values from 1 - 6: sums are 6 + 1=7, 6 + 2 = 8, 6+3 = 9, 6 + 4=10, 6+5 = 11, 6+6 = 12.

Step2: Remove duplicates

The set of sums is {6, 7, 8, 9, 10, 11, 12}.

Answer:

7