Question

How many different strings can be made from the letters in ORONO, using some or all of the letters?

Short answer

The total number of 20 strings can be made from the letters ORONO

Step-by-step solution

Step 1: Use the formula for string factorial

Total number of arrangements of n objects if al are different = n!

If r! of them are same number of ways are given by

\(\begin{array}{l}\frac{{n!}}{{{n_1}!{n_2}!..{n_k}!}} = \frac{{n!}}{{r!}}\\r! = {n_1}!{n_2}!..{n_k}!\end{array}\)

The n! Is string length

r! are outcome of strings

Step 2: Solution of the number of strings made from the letters ORONO 

To count the number of permutations of letters of ORONO with the 3 O's consecutive.

we can treat the 3 consecutive O's as one letter, i.e., count the number of permutations of 1 R,1 N, for a total of 5 "letters".

Here, applied the factorial function

\(\begin{array}{l}n! = 5!\\r! = 3!,1!,1!\\\frac{{n!}}{{r!}} = \frac{{5!}}{{3!.1!.1!}}\\ = 20strings\end{array}\)