We need to find the number of ways to select 7 flowers with at least 2 of each type (roses, tulips, daffodils) from the available stock: 6 roses, 5 tulips, and 4 daffodils.

Consider the possible distributions of flowers:

1. 2 roses, 2 tulips, 3 daffodils: \(\binom{6}{2} \times \binom{5}{2} \times \binom{4}{3} = 600\)
2. 2 roses, 3 tulips, 2 daffodils: \(\binom{6}{2} \times \binom{5}{3} \times \binom{4}{2} = 900\)
3. 3 roses, 2 tulips, 2 daffodils: \(\binom{6}{3} \times \binom{5}{2} \times \binom{4}{2} = 1200\)

Summing these possibilities gives the total number of different bunches:

\(600 + 900 + 1200 = 2700\)