Simple combinatorics

Question

Im having some trouble understanding combinatorics and specifically how "choose" works. I have a homework problem that I think I understand but just want to make sure im not completely off.

The question is...

"We wish to make 6 letter string such that every even letter in an even position is a vowel (no constraints on the odd letters) How many possible strings can we make?" We have access to all 26 letters and repeats are allowed and distinct orderings are different strings.

The answer I am coming up with is...

(26 choose 1) x (5 choose 1) x (26 choose 1) x (5 choose 1) x (26 choose 1) x (5 choose 1)

Am I even on the right track?

Answer 1

Yes, that should be the exact answer unless your teacher is counting 'y' as a vowel to be a jerk

Answer 2

Yes it is a correct approach as for every odd letter position you have 26 alphabets to choose from and for the even ones you have a choice of the 5 vowels.