1. **Stating the problem:**
Andi has 15 identical marbles and wants to put them into 3 containers such that no container is empty. We need to find the number of ways to do this.
2. **Formula used:**
This is a problem of distributing identical items into distinct containers with no container empty. The formula for the number of ways to put $n$ identical items into $k$ distinct containers with no container empty is:
$$\binom{n-1}{k-1}$$
3. **Applying the formula:**
Here, $n=15$ and $k=3$, so the number of ways is:
$$\binom{15-1}{3-1} = \binom{14}{2}$$
4. **Calculating $\binom{14}{2}$:**
$$\binom{14}{2} = \frac{14 \times 13}{2 \times 1}$$
5. **Simplifying:**
$$= \frac{14 \times 13}{\cancel{2} \times 1} = 7 \times 13 = 91$$
6. **Answer:**
The number of ways Andi can put 15 identical marbles into 3 containers with no container empty is **91**.
Marbles Distribution 599Bf5
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