1. **State the problem:** We have a class of 30 kids and want to select 4 of them to write their exam in the library. We need to find how many ways this selection can be done. 2. **Formula used:** Since the order of selection does not matter, this is a combination problem. 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. **Apply the formula:** Here, $n=30$ and $k=4$, so: $$\binom{30}{4} = \frac{30!}{4!(30-4)!} = \frac{30!}{4!26!}$$ 4. **Simplify the factorial expression:** $$\frac{30 \times 29 \times 28 \times 27 \times \cancel{26!}}{4! \times \cancel{26!}} = \frac{30 \times 29 \times 28 \times 27}{4 \times 3 \times 2 \times 1}$$ 5. **Calculate numerator and denominator:** Numerator: $30 \times 29 = 870$, $870 \times 28 = 24360$, $24360 \times 27 = 657720$ Denominator: $4 \times 3 = 12$, $12 \times 2 = 24$, $24 \times 1 = 24$ 6. **Divide to get the final answer:** $$\frac{657720}{24} = 27405$$ **Final answer:** There are $27405$ ways to select 4 kids out of 30 to write their exam in the library.