How many 3-letter sequences can be formed if the second letter must be a vowel (a, e, i, o, or u), and the third letter must be different from the first letter?

120 ways

Step-by-step explanation:

Given that, 3-letter sequences should be formed, where second letter must be a vowel (A, E, I, O, U) and the third letter must be different from the first letter.

There are 26 alphabets in English,

so, firstly let us fix second letter to be one of the vowel

now we are left with 25 alphabets and now let us fix third letter to be a alphabet from remaining 25 alphabets.

now, we are left with 24 alphabets and first letter can be any of these 24 alphabets.

so, there are 24 ways to fill the sequence.

The same thing can be done with other 4 vowels.

so, total number of ways =   5 × 24 = 120 ways.