Question

How many strings with five or more characters can be formed from the letters in SEERESS?

Short answer

The total number of 370 strings can be made from the letters SEERESS

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 SEERESS

To count the number of permutations of letters of SEERESS with the 3 E's consecutive.

we can treat the 3 consecutive E's as one letter, i.e., count the number of permutations of 3 S's (indistinguishable from each other), 1 R, for a total of 7 "letters".

Here, applied the factorial function

\(\begin{array}{l}n! = 7!\\r! = 3!,3!,1!\\\frac{{n!}}{{r!}} = \frac{{7!}}{{3!.3!.1!}}\\ = 370strings\end{array}\)