Question

2. (a) In how many ways, can you arrange the letters in the word “Massachusetts”?

(b) Let’s introduce an additional constraint: a vowel letter has to be the first letter in your arrangement. How many ways can you arrange these letters now?

Answer #1

"Massachusetts" has

1 m, 2 a, 4 s, 1 c, 1 h, 1 u, 1 e, 2 t

Total of 13 letters

(a) The number of ways in which the letters in the word "Massachusetts" can be arranged

= 13!/(2!*4!*2!)

= 64,864,800

(b) There are a total of 4 vowels present in the given word

Number of ways to arrange the letters if the first letter is
**a**

= 12!/(4!*2!)

Number of ways to arrange the letters if the first letter is
**u**

= 12!/(2!*4!*2!)

Number of ways to arrange the letters if the first letter is
**e**

= 12!/(2!*4!*2!)

Thus, total number of ways = 19,958,400

(a) In how many ways, can you arrange the letters in the word
“Massachusetts”?
(b) Let’s introduce an additional constraint: a vowel letter has
to be the first letter in your arrangement. How many ways can you
arrange these letters now?

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?

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.)

a. Find the number of ways to arrange the three letters in the
word CAT in different two-letter groups where CA is different from
AC and there are no repeated letters.
b. Three members from the group of 12 on the board of directors
at Belford Community Hospital will be selected to go to a
convention with all expenses paid. How many different groups of 3
are there?

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...

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?

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?

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

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

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?

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