Question

How many distinct permutations can be made from the letters of the word independence?.

Answer 1

There are 1,663,200 different permutations.

How many different permutations can be made?

First, we need to count the number of different elements in the word independence.

We have 6 different letters.

• i appears only one time.
• n appears 3 times.
• e appears 4 times.
• d appears 2 times.
• p appears one time.
• c appears one time.

For a total of 12 letters. The different number of permutations is given by the factorial of the total number of elements (12) divided by the factorials of the number of repetitions of all the elements. Then we have:

$P = \frac{12!}{1!*3!*4!*2!*1!*1!} = \frac{12!}{3!*4!*2!} = \frac{12*11*10*9*8*7*6*5}{3*2*2} = 1,663,200$

So there are 1,663,200 different permutations.

If you want to learn more about permutations, you can read:

brainly.com/question/12468032