Question

(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?

Answer #1

**Answer:-**

**Given
That:-**

**(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?**

Given,

The word 'DELHI' has 5 letters and all these letters are different.

Total number of words (with or without meaning) That can be formed using all these 5 letters using each letter exactly once

= Number of arrangements of 5 letters taken all at a time

= 5!

= 5 x 4 x 3 x 2 x 1

=120

**(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?**

The word 'ENGINEERING' contains 11 letters, with 3E, 3N, 2G, 2I and IR.

The number of arrangements = 11!/(3!3!2!2!1!)

= 277200

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answer...**

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.)

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.

How many words (both nonsense and sensical) may be formed using
all the letters of the word SENSELESS where N and L are the first
and last letters. (i.e. Case 1: N _ _ _ L and Case 2: L _ _ _ _
N)
The choices given are:
70
35
840
1260
1960

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?

How
many different "words" can you make using all the letters of the
word MISSISSIPPI if
a) there are no restrictions
b) the word must end with an I
c) the word cannot end in an I

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 3-letter passwords can be formed from the letters A
through Z if
a) all letters in the password must be different (i.e ARJ)
b) all letters in the password must be different and they are in
alphabetical order (i.e. AJR)
c) there are no restrictions (i.e. ARR)

In the problems below, A and B can be repeated.
(a) How many 10 letter words can be formed using the letters A and
B? (b) How many of these 10 letter words contain at most 2 A’s?

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