Question

In how many different ways can the letters of the word TEACHER be arranged?
(1) 5040 (2) 2025
(3) 2520
(4) 50400
(5) None of these​

Answer 1

Answer:

(3) 2520

Step-by-step explanation:

Answer 2

Given:

A word- TEACHER

To find:

The number of ways in which the letters of TEACHER can be arranged

Solution:

The number of ways in which the letters of TEACHER can be arranged is 2,520. (Option 3)

We can find the number by following the given process-

We know that the number of possible arrangements can be calculated by using the concept of permutation.

The number of letters in the given word=7

Here, the letter E is repeated twice.

So, the number of different arrangements=P!/n! , where P is the number of letters in the word and n is the number of times any letter is being repeated.

So, the value of n=2 and the value of P is 7.

The number of different arrangements=7!/2!

=7×6×5×4×3×2×1/2×1

=7×6×5×4×3

=2,520

So, there are 2,520 possible ways.

Therefore, the number of ways in which the letters of TEACHER can be arranged is 2,520.