To find the number of possible selections that include at least one member from each year-group, we consider the different combinations of selecting members from each year.

1. Select 1 member from Year 1, 2 members from Year 2, and 2 members from Year 3:

\(7 \times 1 \times 1 = 7\)

2. Select 2 members from Year 1, 2 members from Year 2, and 1 member from Year 3:

\(\binom{7}{2} \times \binom{2}{2} \times \binom{2}{1} = 42\)

3. Select 2 members from Year 1, 1 member from Year 2, and 2 members from Year 3:

\(\binom{7}{2} \times \binom{2}{1} \times \binom{2}{1} = 42\)

4. Select 3 members from Year 1, 1 member from Year 2, and 1 member from Year 3:

\(\binom{7}{3} \times \binom{2}{1} \times \binom{2}{1} = 140\)

Summing these possibilities gives the total number of selections:

\(7 + 42 + 42 + 140 = 231\)