How many three-letter words can be formed using the letters $\;$ $a, \; b, \; c, \; d, \; e$ $\;$ if:
- repetition is allowed;
- repetition is not allowed?
Given: 5 letters $\; a, \; b, \; c, \; d, \; e$
-
Repetition is allowed
The first letter can be selected in $5$ ways.
The second letter can be selected in $5$ ways.
The third letter can be selected in $5$ ways.
$\therefore \;$ Total number of ways of forming three-letter words using the given letters if repetition is allowed is $= 5 \times 5 \times 5 = 125$ ways.
-
Repetition is not allowed
The first letter can be selected in $5$ ways.
The second letter can be selected in $4$ ways.
The third letter can be selected in $3$ ways.
$\therefore \;$ Total number of ways of forming three-letter words using the given letters if repetition is allowed is $= 5 \times 4 \times 3 = 60$ ways.