SOLUTION: ID numbers at a university consist of 1 letter followed by 5 digits, followed by 2 vowels. How many different numbers are possible if: a) letters and digits cannot be repeated. b)

Algebra ->  Probability-and-statistics -> SOLUTION: ID numbers at a university consist of 1 letter followed by 5 digits, followed by 2 vowels. How many different numbers are possible if: a) letters and digits cannot be repeated. b)       Log On


   

Question 321941: ID numbers at a university consist of 1 letter followed by 5 digits, followed by 2 vowels. How many different numbers are possible if: a) letters and digits cannot be repeated. b) letters can be repeated, but digits cannot.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a)There are 26 letters (A-Z), 10 digits (0-9), 5 vowels (A,E,I,O,U)
We'll have to break up the count to include when the first letter is not a vowel and when the first letter is a vowel.
.
.
.
When the first letter is not a vowel.
First slot: Letter - 21 choices
Second slot: Number - 10 choices
Third slot: Number - 9 choices
Fourth slot: Number - 8 choices
Fifth slot: Number -7 choices
Sixth slot: Number - 6 choices
Seventh slot: Vowel - 5 choices
Eigth slot: Vowel - 4 choices
N1=%2821%2A10%21%29%2F3%21
.
.
.
When the first letter is a vowel.
First slot: Letter - 5 choices
Second slot: Number - 10 choices
Third slot: Number - 9 choices
Fourth slot: Number - 8 choices
Fifth slot: Number -7 choices
Sixth slot: Number - 6 choices
Seventh slot: Vowel - 4 choices
Eigth slot: Vowel - 3 choices
N2=5%2A10%2A9%2A8%2A7%2A6%2A4%2A3=10%21%2F2%21
.
.
.
Ntot=N1%2BN2
Ntot=%2821%2A10%21%29%2F3%21%2B10%21%2F2%21
Ntot=10%21%2821%2F6%2B3%2F6%29
Ntot=4%2A10%21=14515200
.
.
.
b)
First slot: Letter - 26 choices
Second slot: Number - 10 choices
Third slot: Number - 9 choices
Fourth slot: Number - 8 choices
Fifth slot: Number -7 choices
Sixth slot: Number - 6 choices
Seventh slot: Vowel - 5 choices
Eigth slot: Vowel - 5 choices
N=26%2A10%2A9%2A8%2A7%2A6%2A5%2A5
N=19656000