A committee of 7 members is to be chosen from 6 artists, 4 singers and 5 writers. In how many ways can this be done if in the committee there must be at least one member from each group and at least 3 artists?

For the given condition, possible ways to select members for a committee of 7 members.

Case 1: (3A, 3S, 1W) = $6C_3\times 4C_3\times 5C_1=20\times 4\times 5=400$

Case 2: (3A, 1S, 3W) = $6C_3\times 4C_1\times 3C_1=20\times 4\times 10=800$

Case 3: (3A, 2S, 2W) = $6C_3\times 4C_2\times 5C_2=20\times 6\times 10=1200$

Case 4: (4A, 2S, 1W) = $6C_4\times 4C_2\times 5C_1=15\times 6\times 5=450$

Case 5: (4A, 1S, 2W) = $6C_4\times 4C_1\times 5C_2=15\times 4\times 10=600$

Case 6: (5A, 1S, 1W) = $6C_5\times 4C_1\times 5C_1=6\times 4\times 5=120$

Thus, the total number of ways is = 400 + 800 + 1200 + 450 + 600 + 120 = 3570