Question

**How many ways can the letters in the word**

**S L U M G U L L I O N**

**be arranged so that the three L’s precede all other
consonants?**

Answer #1

Q6.
In how many different ways can the letters of the word
'MATHEMATICS' be arranged so that the vowels always come
together?

Permutations---------
In how many distinct ways can all the letters of the word
UNBELIEVABLE be arranged amongst themselves if
a) there are no restrictions?
b) the arrangement begins with the letters I V A, in that
order?
c) the arrangements must begin and end with a consonant?

How many distinguishable ways can the letters of the word
COMMUNICATION be arranged in order?

In how many ways can the letters in the word
TRAPEZOIDS be arranged:
a) if you must use 6 different letters?
b) if you use any 6 letters and repetitions are allowed?
c) if the six-letter arrangement must start and end with a
consonant, and repetitions are not allowed?

1. How many permutations are there of the letters in the word
RINSE, if all the letters are used without repetition?
2. In how many distinct ways can the letters of the word SELLS
be arranged?

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...

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?

In how many ways can 3 letters be chosen from M, N, O, P, Q, R,
S, assuming that the order of the choices doesn't matter and that
repeats are not allowed?

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?

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