GPT-4.1
To determine the total number of handshakes when each of the 10 dogs shakes hands with every other dog exactly once, we can use the combination formula for selecting 2 items out of 10, which represents all possible pairs:
\[
\text{Number of handshakes} = C(10, 2) = \frac{10 \times 9}{2} = 45
\]
So, there were **45 handshakes** in total.
**Answer:** 45
To determine the total number of handshakes when each of the 10 dogs shakes hands with every other dog exactly once, we can use the combination formula for selecting 2 items out of 10, which represents all possible pairs:
\[
\text{Number of handshakes} = C(10, 2) = \frac{10 \times 9}{2} = 45
\]
So, there were **45 handshakes** in total.
**Answer:** 45
To determine the total number of handshakes when each of the 10 dogs shakes hands with every other dog exactly once, we can use the combination formula for selecting 2 items out of 10, which represents all possible pairs:
[
\text{Number of handshakes} = C(10, 2) = \frac{10 \times 9}{2} = 45
]
So, there were 45 handshakes in total.
Answer: 45 ...