The number of combinations possible with 4 letters depends on whether the letters can be repeated and the order matters.
If we assume that we have 4 distinct letters and we want to find out how many combinations can be made by selecting any number of these letters without regard to order, we can calculate it as follows:
1. **Choosing 1 letter**: There are 4 choices.
2. **Choosing 2 letters**: We can choose any 2 letters from 4, which can be calculated using the combination formula: C(n, r) = n! / (r!(n - r)!). Here, C(4, 2) = 4! / (2!(4 - 2)!) = 6.
3. **Choosing 3 letters**: Similarly, C(4, 3) = 4! / (3!(4 - 3)!) = 4.
4. **Choosing all 4 letters**: There’s only 1 way, C(4, 4) = 1.
Now we sum these combinations: 4 + 6 + 4 + 1 = 15.
However, if the order of letters matters, and we consider arrangements (permutations) instead, we use the formula: P(n, r) = n! / (n - r)!. If we take 4 distinct letters, the number of ways to arrange all 4 letters would be P(4, 4) = 4! = 24.
In summary:
- Without regard to the order (combinations): 15
- With regard to the order (arrangements): 24