Questions: You pick one card from each set and find the sum. How many different sums are possible?

Transcript text: You pick one card from each set and find the sum. How many different sums are possible?

Solution

Step 1: Identify the Sets

We have two sets of cards:

Step 2: Calculate All Possible Sums

We calculate the sums of all combinations of picking one card from each set. The possible combinations and their corresponding sums are:

\( 1 + 4 = 5 \)
\( 1 + 5 = 6 \)
\( 1 + 6 = 7 \)
\( 2 + 4 = 6 \)
\( 2 + 5 = 7 \)
\( 2 + 6 = 8 \)
\( 3 + 4 = 7 \)
\( 3 + 5 = 8 \)
\( 3 + 6 = 9 \)

Step 3: Identify Unique Sums

The unique sums obtained from the combinations are:

Step 4: Count Unique Sums

The total number of unique sums is \( 5 \).

The number of different sums possible is \\(\boxed{5}\\).

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