1. **Problem statement:** We need to find the number of ways to select 1 boy and 2 girls from a class of 27 boys and 14 girls. 2. **Formula used:** The number of ways to choose $k$ items from $n$ items is given by the combination formula: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ 3. **Step 1:** Calculate the number of ways to select 1 boy from 27 boys: $$\binom{27}{1} = 27$$ 4. **Step 2:** Calculate the number of ways to select 2 girls from 14 girls: $$\binom{14}{2} = \frac{14!}{2!(14-2)!} = \frac{14 \times 13}{2 \times 1} = 91$$ 5. **Step 3:** Since the selections are independent, multiply the two results to get the total number of ways: $$27 \times 91 = 2457$$ **Final answer:** The teacher can make the selection in **2457** different ways.