Question

Matt must take a new code for the lock to his deer lease. It must consist of 3 letters, followed by 5 digits, then 2 letter and 1 more digit. The first letter must be a vowel and the middle digit of the first 5 must be even. If no letter or digit can be repeated, how may code words can be formed?

5x26x25 x10x9x5x8x7 x24x23x6= 2.713x10^11 Is this correct ?

Answer 1

since there are no repeats,
3 letters, 1st vowel: 5*25*24
5 digits, middle even: 5*9*8*7*6
(consider picking the even digit first)
2 letters: 23*22
1 digit: 5

so I get only 114,768,800,00