Determine the number of permutations of the letters of the word "EFFECTIVE"
Rewrite the word as:
"ceeeffitv" we see that it is a 9 letter word in which the letters e and f repeat 3 and 2 times respectively.
The number of permutations is therefore
9!/(3!2!1!1!1!1!)
=30240
Well, let's see. The word "EFFECTIVE" has a total of 10 letters.
First, let's consider the repeated letters. We have 2 "E"s and 2 "F"s.
To find the total number of permutations, we can use the formula:
n! / (r1! * r2! * ... * rk!)
Where n is the total number of objects and r1, r2, etc. are the numbers of repetitions of each object.
So, in this case, the number of permutations would be:
10! / (2! * 2!)
Now, I could write out all the calculations step by step, but that would be a real "EFFORT". So instead, let's just say that the number of permutations is "EFFECTIVELY" 90720.
And remember, this is just a calculation. We're not actually organizing a clown parade here.
To determine the number of permutations of the letters in the word "EFFECTIVE," we can use the formula for permutations:
nPr = n! / (n - r)!
Where n is the total number of items to choose from, and r is the number of items to choose.
In this case, we have 9 letters in the word "EFFECTIVE." Therefore, n = 9.
Since all the letters are unique, we can choose all the letters without repetition. So, r = 9.
Plugging the values into the formula:
nPr = 9! / (9-9)!
= 9! / 0!
= 9! / 1
= 9!
Therefore, the number of permutations of the letters in the word "EFFECTIVE" is 9! (9 factorial).
Calculating 9!:
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 362,880
So, there are 362,880 permutations of the letters in the word "EFFECTIVE."
To determine the number of permutations of the letters in the word "EFFECTIVE," we can use the formula for calculating permutations of objects with repeated elements.
The word "EFFECTIVE" has a total of 10 letters, but there are repeated elements in it. Here, we have 3 "E"s, 2 "F"s, and 2 "E"s again.
To calculate the number of permutations, we'll need to use the following formula:
n! / (n1! * n2! * ... * nk!)
Where:
- n is the total number of objects (letters in this case)
- n1, n2, nk are the number of repetitions for each element type (repeated letters)
In our case:
- n = 10 (total number of letters)
- n1 = 3 (number of "E"s)
- n2 = 2 (number of "F"s)
- n3 = 2 (number of "E"s)
We can substitute these values into the formula to calculate the number of permutations:
10! / (3! * 2! * 2!)
Calculating this expression will give us the answer.