A box contains 10 bulbs, of which just three are defective. If a random sample of five bulbs is drawn , find the probabilities that the sample contains: Exactly on defective bulb. Exactly two defective bulbs. No defective bulbs.

Explanation

To solve the problem, we will calculate the probabilities for three different cases: exactly 1 defective bulb, exactly 2 defective bulbs, and no defective bulbs in a sample of 5 drawn from a box containing 10 bulbs (3 defective and 7 non-defective).

### Step-by-Step Solution:

**Step 1: Total Ways to Choose 5 Bulbs**
- The total number of ways to choose 5 bulbs from 10 is given by the combination formula \( \binom{n}{r} \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.
- Thus, the total ways to choose 5 bulbs from 10 is:
\[
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