how many arrangements can be formed from all the letters in the word parallel?
you have 3 l's, 2 a's, and 3 other letters.
so no of arrangement = 8!/(3!2!) = 3360
To find the number of arrangements that can be formed from the word "parallel," we can use the concept of permutations.
The word "parallel" has 8 letters. Let's start by assuming that all the letters are distinct. So, we have a total of 8 distinct letters.
The number of arrangements of n distinct objects is given by n factorial (n!). The factorial of a number is the product of all positive integers less than or equal to that number.
In this case, the number of arrangements of the 8 distinct letters in the word "parallel" is 8!.
However, we have to consider the repeated letters. The letter 'l' appears twice in the word. This means that the arrangements that have the 'l' letters swapped would be identical.
To correct this, we need to divide by the factorial of the number of repeated letters. In this case, we need to divide by 2! since there are two identical 'l' letters.
So, the total number of arrangements can be calculated as:
8! / 2!
Calculating this:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
2! = 2 x 1 = 2
Now, dividing:
40,320 / 2 = 20,160
Therefore, there are 20,160 possible arrangements that can be formed from all the letters in the word "parallel".