Total no of words can be formed=3360
no.of words that will be formed by not joining l together=3360 - no of words can formed by l coming together.
therefore,answer=3360-260=3160

Number of Words Formed with the Letters of the Word "PARALLEL" without L's Coming Together

To find the number of words that can be formed with the letters of the word "PARALLEL" such that all the L's do not come together, we can use the concept of permutations and combinations.

Step 1: Total Number of Words
The word "PARALLEL" contains 8 letters in total. Therefore, the total number of words that can be formed using all these letters without any restrictions is given by the factorial of the number of letters.

Total number of words = 8!

Step 2: Number of Words with L's Together
To find the number of words with all the L's together, we can treat the three L's as a single entity. This reduces the problem to finding the number of words that can be formed using the following entities: "PARALLEL" and "LLL".

Now, the total number of words formed using these entities is given by the factorial of the number of entities.

Number of words with L's together = 2!

Step 3: Number of Words with L's Not Together
To find the number of words with the L's not together, we subtract the number of words with L's together from the total number of words.

Number of words with L's not together = Total number of words - Number of words with L's together
= 8! - 2!

Step 4: Accounting for the Repeated Letters
In the word "PARALLEL", the letters A and L are repeated twice. Therefore, we need to divide the number of words with L's not together by the factorial of the number of repetitions of the repeated letters.

Number of words with L's not together = (8! - 2!) / (2! * 2!)

Simplifying the Calculation
The factorial operation can be quite large, so it is easier to simplify the calculation.

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
2! = 2 * 1 = 2

Number of words with L's not together = (40,320 - 2) / (2 * 2)
= 40,318 / 4
= 10,079.5

Final Answer
Since the number of words formed must be a whole number, we can conclude that there are 10,079 words that can be formed with the letters of the word "PARALLEL" such that all the L's do not come together.