Question

The number of ways in which the letters of the word 'ERASER' can be arranged so that both E's are never together, is​

Answer 1

Answer:

The number of ways in which the letters of the word 'ERASER' can be arranged so that both E's are never together is 12.

Question : The number of ways in which the letters of the word 'ERASER' can be arranged so that both E's are never together, is​

Step-by-step explanation:

From the above question,

They have given :

The number of ways in which the letters of the word 'ERASER' can be arranged so that both E's are never together is found by using the formula for permutations with repetition: n! / (r1! * r2! * ... * rk!).

Where n is the total number of letters, and r1, r2, ..., rk are the number of occurrences of each letter.

In this case, n = 5 and r1 = 2 (for the two E's) and r2 = 1 (for each of the other three letters).

Thus, the number of ways in which the letters of the word 'ERASER' can be arranged so that both E's are never together is,

5! / (2! * 1! * 1! * 1!) = 4! / 2! = 12

1.  Count the total number of letters in the word ERASER, which is 5.

2.  Count the number of occurrences of each letter, which is 2 for the letter E and 1 for each of the other three letters (R, A, and S).

3.  Use the formula for permutations with repetition: n! / (r1! * r2! * ... * rk!), where n is the total number of letters, and r1, r2, ..., rk are the number of occurrences of each letter.

4.  Substitute the values from steps 1 and 2 into the formula: 5! / (2! * 1! * 1! * 1!) = 4! / 2! = 12.

5.  The number of ways in which the letters of the word 'ERASER' can be arranged so that both E's are never together is 12.

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