Question

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)

Answer #1

a) If all letters in the password is different, then we have to

choose 3 letters out of 26 letters to construct the

password. It can be done in ways. Also the three

letters can interchange between themselves in 3! ways.

So, total number of ways = 3! = 15600 ways. (Ans).

b) We can choose 3 letters out of 26 letters in ways.

Now the three letters can again interchange between

themselves in 3! = 6 ways, but out of 6 ways, only 1 will be

in alphabetical order. So, total number of ways =

= 2600. (Ans).

c) If there are no restrictions, then the 1st letter can be

chosen in 26 ways, the 2nd in 26 ways and the 3rd also in

26 ways. So, total number of ways = = 17576. (Ans).

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?

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?

Determine how many different computer passwords are possible if
(a) the digits and letters can be repeated, and (b) if the digits
and letters cannot be repeated.
i. 4 digits followed by 2 letters
ii. 5 digits followed by 1 letter.
iii. 3 digits followed by 3 letters

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 different 4-letter radio station call letters can be
made
a. If the first letter must be K, Z, or P and no letter may be
repeated
b. if repeats are allowed (but the first letter is K, Z, or
P)?
c. How many of the 4-letter radio station call letters
(starting with K, Z, or P) have no repeats and end with the letter
J?

1) Assume that a password can contain upper and lower-case
letters (26), digits, and special characters from the set { !, #,
$, %, &, * }. Furthermore, each password must start with a
letter and must contain at least one digit and one special
character. How many different six-character passwords can be formed
according to this specification?

(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 different 6-letter radio station call letters can be
made a. if the first letter must be G or X and no letter may be
repeated? b. if repeats are allowed (but the first letter is G or
X)? c. How many of the 6-letter radio station call letters
(starting with G or X) have no repeats and end with the letter
R?

How many passwords of 5 characters can be made if each password
must start with two digits and end with three letters. The digits
will be with replacement and the letters will be without
replacement.

A computer password consists of: • letters {a, A, 6, B,
...,2,Z}, • digits {0, 1,...,9), or = 16 • special characters
{!,@,#,$,%}. In addition, a password must • contain at least one
upper case letter, • contain at least one special character. How
many passwords of length 8 are possible?

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