Question

how many strings of length 14 of lower case letters from the English alphabet can be formed, if the first two letters cannot Abe both vowels and the last letter must be a consonant?

Answer #1

how many
strings of 8 lower case letters from the English alphabet contain
the letter a? how many strings if 8 lower case letter from the
english alphabet contain the letter a and b?

how many
strings of 7 lower case letters from the wnglish alphabet contain
the letter a? How many strings of 7 lower case letters from the
english alphabet contain the letter a and b?

How many strings of seven lowercase letters from the English
alphabet contain
a. the letters a and b in consecutive positions with a preceding
b, with all the letters distinct?
b. the letters a and b, where a is somewhere to the left of b in
the string, with all the letters distinct?

you are trying to form a 6-letter code from the 26 letters of
the alphabet. suppose your code must follow the following
rules:
* the first two letters must be different vowels ( AEIOU). (
this means no repeats.)
* the next two letters have no restrictions in other words, any
letter is fine.)
* the last two letters cannot be a vowel, but they could
repeat.
how many different codes are possible?

a) How many four-letter words can be formed from the letters of
the word TAUDRY if each letter can only be used one time in a word?
Y is NOT considered a vowel in this word.
b) How many contain all the vowels?
c) How many contain exactly three consonants?
d) How many of them begin and end in a consonant?
e) How many contain both D and Y?

a) How many four-letter words can be formed from the letters of
the word TAUDRY if each letter can only be used one time in a word?
Y is NOT considered a vowel in this word.
b) How many contain the letter Y?
c) How many contain all the vowels?
d) How many contain exactly three consonants?
e) How many of them begin and end in a consonant?
f) How. many begin with a D and end in a vowel...

How many words can be formed by arranging the letters of the
word “EQUATIONS” such that the first letter of the word is a vowel
and the last position is a consonant letter? (Note: The words thus
formed need not be meaningful.)

How many different 5 letter computer passwords can be made using
the English alphabet. Case does not matter.

How many strings of
five uppercase English letters are there
(a) that start with the letters BO (in that order), if letters can
be repeated?
(b) if letters can be repeated?
(c) that start and end with the letters BO (in that order), if
letters can be repeated?
(d) that start or end with the letters BO (in the order), if
letters can be repeated? (inclusive or)

Consider mini-alphabet made of just letters {a, b, c, d, e}. How
many “words” (i.e., strings of letters from that alphabet, whether
they correspond to meaningful words or not) are there of length n,
for n≥1 ? Use mathematical induction to prove your answer.

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