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)
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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) (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.
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.
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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
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.
.
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
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.
.
.
.
.
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
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