## Task B-4.5.

In the Croatian language class, children competed in forming five-letter words. They could only use the letters of the word SNOW (they could use one letter multiple times). The only condition was that each word must use the letter E exactly twice. What is the maximum number of different words (not necessarily meaningful) that someone could form?
## Solution.

First, we will place the two letters E in two positions in the word. The first E can be placed in 5 ways, and the second in 4 ways. This would be a total of 20 ways, but we have counted each arrangement twice, as we do not distinguish which E is in which position. Therefore, we need to divide this number by 2. The two letters E can be placed in 10 ways.

On each of the remaining three positions, we can write any of the remaining five letters (S, N, I, J, G), which we can do in $5 \cdot 5 \cdot 5=5^{3}$ ways.

In total, it is possible to form $10 \cdot 5^{3}=1250$ words.

Note: The student can immediately write the solution $\binom{5}{2} \cdot 5 \cdot 5 \cdot 5=1250$ and receive full marks.