How many 3 letter arrangements can you make while making the first and the third letter one of the 21 constants and the middle letter one of the 5 vowels {a,e,i,o,u} . {two such arrangments to use are KOM and XAX?
To find the number of 3-letter arrangements that can be made using one consonant as the first letter, one vowel as the middle letter, and another consonant as the third letter, you can use the counting principle.
First, determine the number of choices for each position:
1. For the first position, you can choose any one of the 21 consonants.
2. For the second position (middle letter), you can choose any one of the 5 vowels.
3. For the third position, you can choose any one of the 21 consonants.
Using the counting principle, multiply the number of choices for each position:
Total number of arrangements = Number of choices for position 1 × Number of choices for position 2 × Number of choices for position 3
Total number of arrangements = 21 × 5 × 21
Total number of arrangements = 2,205
So, there are 2,205 possible 3-letter arrangements given the conditions.