The question is asking for the number of different words that can be formed using the letters of the word "EDUCATION" with the condition that the letters A and T are never together.

Here's how to solve it:

Step 1: Find the total number of arrangements without any restrictions. The word "EDUCATION" has 9 letters, so the total number of arrangements is 9! (9 factorial).

Step 2: Find the number of arrangements where A and T are together. Treat "AT" or "TA" as a single letter, then we have 8 letters in total. So the number of arrangements is 8! * 2! (because "AT" or "TA" can be arranged in 2 ways).

Step 3: Subtract the number of arrangements where A and T are together from the total number of arrangements. This gives the number of arrangements where A and T are not together.

So, the correct answer is 9! - 8! * 2! = 7! X 8P2.

Question

The question is asking for the number of different words that can be formed using the letters of the word "EDUCATION" with the condition that the letters A and T are never together.

Here's how to solve it:

Step 1: Find the total number of arrangements without any restrictions. The word "EDUCATION" has 9 letters, so the total number of arrangements is 9! (9 factorial).

Step 2: Find the number of arrangements where A and T are together. Treat "AT" or "TA" as a single letter, then we have 8 letters in total. So the number of arrangements is 8! * 2! (because "AT" or "TA" can be arranged in 2 ways).

Step 3: Subtract the number of arrangements where A and T are together from the total number of arrangements. This gives the number of arrangements where A and T are not together.

So, the correct answer is 9! - 8! * 2! = 7! X 8P2.

Knowee AI · Accepted Answer

The question is asking for the number of different words that can be formed using the letters of the word "EDUCATION" with the condition that the letters A and T are never together.

Here's how to solve it:

Step 1: Find the total number of arrangements without any restrictions. The word "EDUCATION" has 9 letters, so the total number of arrangements is 9! (9 factorial).

Step 2: Find the number of arrangements where A and T are together. Treat "AT" or "TA" as a single letter, then we have 8 letters in total. So the number of arrangements is 8! * 2! (because "AT" or "TA" can be arranged in 2 ways).

Step 3: Subtract the number of arrangements where A and T are together from the total number of arrangements. This gives the number of arrangements where A and T are not together.

So, the correct answer is 9! - 8! * 2! = 7! X 8P2.

Select the correct answerHow many different words can be formed using the letters of the word “EDUCATION‘ such that, The letters A and T are never together?Options7! X 8P22 X 7!7!7! X 8P4

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