Question

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?

Answer #1

We need 6 letter radio station call letters

a) 1st letter is choosed from letters G or X as 2c1 =2

No letters are repeated. So the next 5 letters chooses from the remaining (26-1=25) 25 letters as

= 25c1 × 24c1× 23c1 × 22c1×21c1

= 25×24×23×22×21

So 6 letters formed as = 2 × 25×24×23×22×21

= 12,751,200 ways

b) 1st letter is choosen from G or X as 2c1 ways

And repetition is allowed then the next 5 letters chooses from 26 letters as 26c1×26c1×26c1×26c1×26c1

So 6 letters formed as

= 2× 26×26×26×26×26

=23,762,752 ways

C) 1st letter is choose from G or X as 2c1 ways and no repeat and the last letter is must R it chooses as 1 way. then the remaining 4 letters chooses from 24 letters ( not G or X and R)

as 24c1×23c1×22c1×21c1

= 24×23×22×21ways

Then the 6 letters are

= 2× 24×23×22×21×1

= 510,048 ways

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?

How
many different 4-letter radio station call letters can be made if
thr first letter must be K or W, repeats are allowed, but the call
letters cannot end in an O?

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?

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 different letter arrangements can be made
from the letters of the word
KALAMAZOO

you are trying to form a 6-letter code from the 26 letters of
the alphabet. suppose your code must follow the following
rules:
* the first two letters must be different vowels ( AEIOU). (
this means no repeats.)
* the next two letters have no restrictions in other words, any
letter is fine.)
* the last two letters cannot be a vowel, but they could
repeat.
how many different codes are possible?

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letters of the alphabet?
2. How many strings of 6 letters are there – if the letters
cannot be repeated?
3. How many strings of 6 letters are there – if the letters can
be repeated?

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 letter codes can be created with the letters M, E, O, W
if letters can be repeated

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

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