Question

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?

Answer #1

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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.)

5 -letter "words" are formed using the letters A, B, C, D, E, F,
G. How many such words are possible for each of the following
conditions?
a) No condition is imposed.
b) No letter can be repeated in a word.
c) Each word must begin with the letter A.
d) The letter C must be at the end.
e) The second letter must be a vowel.

(a) How many words with or without meaning, can be formed by
using all the letters of the word, ’DELHI’ using each letter
exactly once?
(b) How many words with or without meaning, can be formed by
using all the letters of the word, ’ENGINEERING’ using each letter
exactly once?

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?

How many 3 letter words (both nonsense and sensical) may be
formed out of the letters of the word 'PROBABILITY'?
The choices given are:
a. 210
b. 432
c. 552
d. 531
e. 1960

how many arrangements can be made using the letters of
"EQUATIONS" provided that the vowels always remain in the same
order? NOTE: consonant letters can go in between the vowels; the
vowels only need to be in the exact same order and do NOT have to
be ALWAYS adjacent to each other.
e.g. "ETQUAIONS" would be one of the many
possibilities; note that, here there are consonants in between the
vowels but the order of the vowels is the same.

The Hawaiian alphabet has twelve letters: five vowels (a, e, i,
o, and u) and seven consonants (h, k, l, m, n, p, and w). For the
purpose of this exercise we will define an n–letter “word” as an
ordered collection of n of these twelve letters with repeats
allowed. Obviously, most such “words” will be nonsense words.
What is the probability a randomly selected four–letter “word”
contains exactly one consonant?

4. The Hawaiian alphabet has twelve letters: five vowels (a, e,
i, o, and u) and seven consonants (h, k, l, m, n, p, and w). For
the purpose of this exercise we will define an n–letter “word” as
an ordered collection of n of these twelve letters with repeats
allowed. Obviously, most such “words” will be nonsense words.
e) What is the probability a randomly selected
four–letter “word” contains exactly one consonant?

How many 55-letter code words can be formed from the letters U,
G, S, E, A if no letter is repeated? If letters can be repeated?
If adjacent letters must be different?

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