) How many different three-letter initials can people have: , (b) How many different three-letter initials with none of the letters repeated can people have: , (c) How many different three-letter initials with letters repeated begin with an X: , (d) How many different three-letter initials begin with a F and end in a D:

Solution :

a).

The different three letter initials that people have is :

= 26 x 26 x 26

=

=

b). The first place to be fill in26 ways.

The second place to be filled in 25 ways

The third place to be filled in 24 ways.

Therefore, total number of three letter initial with no repetition is :

= 26 x 25 x 24

=

c). The total number of three letter initial begin with X = 1 x 26 x 26

                                                                                          =

d). The total number of the three letter initials that begin with letter 'F' an end with letter 'D' is = 1 x 26 x 1

                                 =

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$12. that is my answer.