How many 3 letter words can you make from the letters A,B,C and D, where letters cannot be repeated and are in alphabetical order?

To determine how many 3-letter words can be made from the letters A, B, C, and D, where letters cannot be repeated and must be in alphabetical order, follow these steps:

1. Identify the available letters: A, B, C, D.
2. Choose 3 letters out of the 4: Since the letters must be in alphabetical order and cannot be repeated, we need to select 3 out of the 4 letters.

The number of ways to choose 3 letters out of 4 is given by the combination formula $\binom{n}{k}$, where $n$ is the total number of items to choose from, and $k$ is the number of items to choose.

Here, $n = 4$ and $k = 3$.

$\binom{4}{3} = \frac{4!}{3!(4-3)!} = \frac{4!}{3! \cdot 1!} = \frac{4 \times 3!}{3! \times 1} = 4$

So, there are 4 ways to choose 3 letters out of 4.

3. List the combinations: Since the letters must be in alphabetical order, the combinations are:
   • ABC
   • ABD
   • ACD
   • BCD

Therefore, there are 4 possible 3-letter words that can be made from the letters A, B, C, and D, where letters cannot be repeated and are in alphabetical order.