how many different 10-letter words (real or imaginary) can be formed from the letters in the word MONOCHROME?
nevermind got the answer already
302400
To determine the number of different 10-letter words that can be formed from the letters in the word MONOCHROME, we can use the concept of permutations.
The word MONOCHROME has a total of 10 letters.
First, let's count the number of times each letter appears in the word:
- M: 1
- O: 3
- N: 1
- C: 1
- H: 1
- R: 1
- E: 1
Now we can calculate the total number of permutations:
Total Permutations = (Total Letters)! / (Frequency of M! x Frequency of O! x Frequency of N! x Frequency of C! x Frequency of H! x Frequency of R! x Frequency of E!)
Plugging in the values:
Total Permutations = 10! / (1! x 3! x 1! x 1! x 1! x 1! x 1!)
Calculating further:
Total Permutations = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (1 x 2 x 3 x 1 x 1 x 1 x 1 x 1 x 1)
Total Permutations = 3,628,800 / (6)
Total Permutations = 604,800
Therefore, there are 604,800 different 10-letter words that can be formed from the letters in the word MONOCHROME (real or imaginary).
To find the number of different 10-letter words that can be formed from the letters in the word "MONOCHROME," we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, we want to find the number of ways to arrange the 10 letters in "MONOCHROME."
To start, we need to determine how many times each letter appears in the word "MONOCHROME" to account for repeated letters. In this case, the word "MONOCHROME" has the following letters:
- M: 1 time
- O: 3 times
- N: 1 time
- C: 1 time
- H: 1 time
- R: 1 time
- E: 1 time
Now we can calculate the number of different 10-letter words.
Step 1: Find the total number of letters available (N) without considering any repetitions. In this case, N = 10.
Step 2: Calculate the number of permutations using the formula:
P = N! / (n1! * n2! * n3! * ... * nk!)
Where P is the total number of permutations, N is the total number of letters, and n1, n2, ... nk represent the number of times each letter appears.
Substituting the values, we have:
P = 10! / (1! * 3! * 1! * 1! * 1! * 1! * 1!)
P = 10! / (1 * 3 * 1 * 1 * 1 * 1 * 1)
P = 10! / 3
P = 3,628,800 / 3
P ≈ 1,209,600
Therefore, there are approximately 1,209,600 different 10-letter words (real or imaginary) that can be formed from the letters in the word "MONOCHROME".