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

Answer

Explanation:

Step1: Determine number of outcomes for each action

A die has 6 outcomes, picking a card has 2 outcomes, and spinning the spinner has 2 outcomes.

Step2: Calculate total number of combinations

By the fundamental counting principle, the total number of combinations of the three - actions is (6\times2\times2= 24).

Step3: Find the minimum and maximum sums

The minimum sum occurs when we get 1 on the die, 5 on the card, and 3 on the spinner: (1 + 5+3=9). The maximum sum occurs when we get 6 on the die, 6 on the card, and 4 on the spinner: (6 + 6+4 = 16).

Step4: Analyze possible sums

The possible sums range from 9 to 16. The number of integers from 9 to 16 is (16 - 9+1=8).