How many different sequences of length 5 are there in a three-letter alphabet "cat"? - briefly
There are (3^5 = 243) different sequences of length 5 in a three-letter alphabet "cat". This is because each position in the sequence can be filled with one of the three letters ('c', 'a', or 't'), and there are five positions to fill.
How many different sequences of length 5 are there in a three-letter alphabet "cat"? - in detail
To determine the number of different sequences of length 5 in a three-letter alphabet "cat," we need to consider each position in the sequence and the possibilities for each letter to occupy that position.
First, let's understand the composition of our alphabet. The alphabet consists of three unique letters: 'c', 'a', and 't'. Each position in the 5-letter sequence can be filled by any one of these three letters. This principle holds true for all five positions in the sequence.
To calculate the total number of different sequences, we apply the rule of multiplication for independent events. For each position in the sequence, there are 3 possible choices (c, a, or t). Since there are 5 positions to be filled independently:
[ \text{Total number of sequences} = 3 \times 3 \times 3 \times 3 \times 3 ]
Carrying out the multiplication gives us:
[ 3^5 = 243 ]
Therefore, there are 243 different sequences of length 5 that can be formed using the three-letter alphabet "cat."