Passcodes with repetition

Question

How many ways are there to form a five-letter codeword satisfying the following conditions using only the letters a to z (all lowercase). Repetitions are allowed.

1. No restrictions.
2. The codeword must start with a vowel.
3. The codeword must end with a consonant.
4. The codeword starts with two vowels and end with a consonant.

Solution

1. ${26}^5=\mathrm{11,881,376}∎$
2. $5\times {26}^4=\mathrm{2,284,880}∎$
3. $21\times {26}^4=\mathrm{9,596,496}∎$
4. $5^2\times 21\times {26}^2=\mathrm{354,900}∎$