Kristen and Christopher were playing a board game. They used a spinner with 4 spaces labeled 1, 2, 3, and 4. Each player was allowed 3 consecutive spins. They could move pieces on a board game only if the total of the 3 spins equaled 5.
How many possible combinations could they spin?
How many combinations equaling 5 could they spin?
1+1+3 = 5
1+2+2 = 5
And you can shuffle those around, making
3+3 = 6 ways to spin 5
To find the possible combinations and the combinations equaling 5 that they could spin, we can use the concept of combinations with repetition.
In this case, we have a spinner with 4 spaces labeled 1, 2, 3, and 4, and each player is allowed 3 consecutive spins.
To find the number of possible combinations, we can calculate it using the formula for combinations with repetition:
C(n + r - 1, r)
Where n is the number of options (in this case, 4) and r is the number of consecutive spins (in this case, 3).
So for this problem, the number of possible combinations they could spin is:
C(4 + 3 - 1, 3) = C(6, 3) = 20
Now, let's find the number of combinations that equal 5. We need to identify the combinations of spins that add up to 5.
To do this, we can create a table to list all possible combinations of 3 spins and calculate the sum for each combination:
Spin 1 | Spin 2 | Spin 3 | Sum
1 | 1 | 1 | 3
1 | 1 | 2 | 4
1 | 1 | 3 | 5
1 | 1 | 4 | 6
1 | 2 | 1 | 4
1 | 2 | 2 | 5
1 | 2 | 3 | 6
1 | 2 | 4 | 7
1 | 3 | 1 | 5
1 | 3 | 2 | 6
1 | 3 | 3 | 7
1 | 3 | 4 | 8
1 | 4 | 1 | 6
1 | 4 | 2 | 7
1 | 4 | 3 | 8
1 | 4 | 4 | 9
2 | 1 | 1 | 4
2 | 1 | 2 | 5
2 | 1 | 3 | 6
2 | 1 | 4 | 7
2 | 2 | 1 | 5
2 | 2 | 2 | 6
2 | 2 | 3 | 7
2 | 2 | 4 | 8
2 | 3 | 1 | 6
2 | 3 | 2 | 7
2 | 3 | 3 | 8
2 | 3 | 4 | 9
2 | 4 | 1 | 7
2 | 4 | 2 | 8
2 | 4 | 3 | 9
2 | 4 | 4 | 10
3 | 1 | 1 | 5
3 | 1 | 2 | 6
3 | 1 | 3 | 7
3 | 1 | 4 | 8
3 | 2 | 1 | 6
3 | 2 | 2 | 7
3 | 2 | 3 | 8
3 | 2 | 4 | 9
3 | 3 | 1 | 7
3 | 3 | 2 | 8
3 | 3 | 3 | 9
3 | 3 | 4 | 10
3 | 4 | 1 | 8
3 | 4 | 2 | 9
3 | 4 | 3 | 10
3 | 4 | 4 | 11
4 | 1 | 1 | 6
4 | 1 | 2 | 7
4 | 1 | 3 | 8
4 | 1 | 4 | 9
4 | 2 | 1 | 7
4 | 2 | 2 | 8
4 | 2 | 3 | 9
4 | 2 | 4 | 10
4 | 3 | 1 | 8
4 | 3 | 2 | 9
4 | 3 | 3 | 10
4 | 3 | 4 | 11
4 | 4 | 1 | 9
4 | 4 | 2 | 10
4 | 4 | 3 | 11
4 | 4 | 4 | 12
From the table above, we can see that there are 4 combinations of spins that add up to 5: (1, 1, 3), (1, 2, 2), (2, 1, 2), and (3, 1, 1).
Therefore, the number of combinations equaling 5 that they could spin is 4.