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# Sets

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1. (Counting words). How many 4-letter words do not begin
or end with a vowel?
[Here the alphabet is assumed to be {a, b, c, . . . , z} and the set of vowels is
{a, e, i, o, u}. A (mathematical) word is any string of letters: it need not be
a word in any language.]
rep for good help
2. surely you could say there are 21 different possibilities for the 1st and 4th letters, and 26 different possibilities for the 2nd and 3rd letters.. so there are 21*21*26*26 possibilities?

not sure if thats correct just a quick idea
3. (Original post by just george)
surely you could say there are 21 different possibilities for the 1st and 4th letters, and 26 different possibilities for the 2nd and 3rd letters.. so there are 21*21*26*26 possibilities?

not sure if thats correct just a quick idea
ok how sure are you?
4. well between 0 and 9 inclusive there are 10 digits.. and there are 100 2 digit numbers if you include 00, so in that case there are 10 possible 1st digits and 10 possible 2nd digits giving 10*10 possible 2 digit numbers.. there are also 10*10*10 3 digit numbers and 10*10*10*10 4 digit numbers. so by the same logic my thing works, providing there is no problem with repeating letters (e.g. BBBB is a word?) etc..

short version.. pretty sure
5. (Original post by just george)
well between 0 and 9 inclusive there are 10 digits.. and there are 100 2 digit numbers if you include 00, so in that case there are 10 possible 1st digits and 10 possible 2nd digits giving 10*10 possible 2 digit numbers.. there are also 10*10*10 3 digit numbers and 10*10*10*10 4 digit numbers. so by the same logic my thing works, providing there is no problem with repeating letters (e.g. BBBB is a word?) etc..

short version.. pretty sure
ok cheers!

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