Question:

Step 1: Verify option (a). Choose 3 Indian classics from 6 for top 5: $\binom{6}{3}$ ways. Choose 2 western from 4 for top 5: $\binom{4}{2}$ ways. Arrange top 5: $5!$ ways. Arrange remaining 5: $5!$ ways. Total $= \binom{6}{3}\binom{4}{2}(5!)(5!) = 20 \cdot 6 \cdot 120 \cdot 120 = 120 \cdot 120 \cdot 120 = (5!)^3$. ✓ Step 2: Verify option (b). Top rank goes to an Indian classic: choose 1 from 6 ($6$ ways), arrange remaining 9 ($9!$ ways). Total $= 6 \cdot 9!$. ✓ Step 3: Verify option (c). Treat 4 western songs as a block: arrange the block internally ($4!$ ways), arrange 7 items (6 Indian + 1 block) ($7!$ ways). Total $= 4! \cdot 7!$. ✓ Step 4: Verify option (d). Fix the 6 Indian classics in a specified order: choose 4 positions from 10 for western songs and arrange them: ${}^{10}P_4$ ways (the remaining 6 positions are fixed for Indian classics in order). Total $= {}^{10}P_4$. ✓