2. In how many ways can you form 3-letter "words" from the letters of "Adelphi" so that the first and last letters are vowels? No repeats allowed. Explain your answer

The total number of ways are 30.

Step-by-step explanation:

Consider the provided information.

We need to write 3-letter "words" from the letters of "Adelphi" so that the first and last letters are vowels.

The number of letters in "Adelphi" = 7

The number of vowels are = 3

It is given that the first and last letters are vowels.

For first letter we have 3 choices, and for the last letter we have 2 choices as repetition is not allowed.

If we have selected first and last letter that means now we have 5 letters for the middle letter. (7-2=5)

So the number of possible choices for the 2nd letter is 5.

Hence, the total number of ways are: 3*5*2 = 30 ways