How many different symbolic sequences of length 5 are there in a three-letter alphabet cat o? - briefly
In a three-letter alphabet consisting of the letters "c", "a", and "t", the number of different symbolic sequences of length 5 can be calculated by raising the number of available choices (3) to the power of sequence length (5). This results in (3^5 = 243) unique sequences.
How many different symbolic sequences of length 5 are there in a three-letter alphabet cat o? - in detail
To determine the number of different symbolic sequences of length 5 in a three-letter alphabet consisting of the letters "c", "a", and "t", we can employ combinatorial principles. Each position in the sequence can be filled with one of the three available letters. Since there are no restrictions on repetition, each of the five positions can independently be occupied by any of the three letters.
Let's break down the calculation step-by-step:
- First Position: There are 3 choices (c, a, t).
- Second Position: Regardless of the choice for the first position, there are still 3 choices available.
- Third Position: Again, 3 choices remain regardless of the previous selections.
- Fourth Position: As before, 3 choices are available.
- Fifth Position: Similarly, 3 choices can be made.
Since each position is independent of the others, we multiply the number of choices for each position to find the total number of sequences:
[ 3 \times 3 \times 3 \times 3 \times 3 = 3^5 ]
Calculating (3^5):
[ 3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243 ]
Therefore, there are 243 different symbolic sequences of length 5 that can be formed using the three-letter alphabet "cat o".