Question

How many palindromes of length 5 can you form using letters with the following properties: they start with a consonant, and the consonants and vowels alternate; no letter appears more than twice. (Note: assume letters "a", "e", "i", "o", and "u" are the vowels of the English alphabet). please help

Answer 1

2100

Step-by-step explanation:

For palidrome 1st and 5th letter have to be the same, similarly the 2nd and 4th letter have to be the same.ex: TENET

1st letter can have 21 possibilities ( any consonant)

5th letter can have 1 value same as the 1st letter (since palindrome)

2nd letter is a vowel has 5 possible values

4th letter is a vowel has to have same value as 2nd (since palidrome)

3rd letter can have only 20 possibilities , because we cannot repeat a letter more than twice, we cannot pick the letter in the first position.

21 * 5 * 20 * 1 * 1 = 2100