To find the number of ways a delegation of 3 can be chosen from 5 men and 3 women, with at least 1 man and 1 woman included, we can consider the possible combinations based on the given conditions.

1. Choose 1 man and 2 women:

Number of ways to choose 1 man from 5: \(5\)

Number of ways to choose 2 women from 3: \(\binom{3}{2} = 3\)

Total ways for this case: \(5 \times 3 = 15\) ways

2. Choose 2 men and 1 woman:

Number of ways to choose 2 men from 5: \(\binom{5}{2} = 10\)

Number of ways to choose 1 woman from 3: \(3\)

Total ways for this case: \(10 \times 3 = 30\) ways

Adding the two cases together: 15 + 30 = 45 ways