Question

how many different arrangements can be made with the letter of the word "GENTLEMEN"?​

Answer 1

Answer:

9 letters because gentleman letters you see

Answer 2

Given:

A word- GENTLEMEN

To find:

The number of different arrangements that can be made of the letters of this word

Solution:

We can find the solution by following the given process-

We know that the question is based on the concept of permutations.

The number of letters in the word GENTLEMEN=9

But some letters are being repeated.

E is repeated 3 times, N is repeated 2 times.

So, the number of arrangements= Factorial of the total number of letters/ Product of factorial of the number of times the letters are repeated

The number of arrangements= 9!/3!×2!

=9×8×7×6×5×4×3×2×1/3×2×2×1

=9×8×7×5×4×3

=72×21×20

=30,240

Therefore, 30,240 different arrangements can be made with the letters of the word "GENTLEMEN".