How many anagrams can be created from the word 'metamorphosis' if the new words do not need to be meaningful? (Anagram is just rearangment of letters)
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
![**Question**: How many anagrams can be created from the word 'metamorphosis' if the new words do not need to be meaningful? (Anagram is just a rearrangement of letters)
**Explanation**: An anagram involves rearranging the letters of a word to form new sequences. In this context, any sequence, regardless of whether it forms a valid word, is considered.
The word 'metamorphosis' consists of 12 letters:
- M, E, T, A, M, O, R, P, H, O, S, I
To find the number of anagrams, calculate the factorial of the total number of letters and then divide by the factorials of the frequencies of each repeated letter.
1. Total letters = 12
2. Frequency of each letter: M=2, O=2
Formula:
\[ \frac{12!}{2! \times 2!} \]
This formula accounts for dividing by the factorial of repeated letters (M and O) to prevent counting the same arrangements multiple times.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd979ca11-a879-4042-955f-84151bb5000b%2F1346b8ba-c9ce-44f3-804a-7e5765f51193%2Fplso5nh_processed.jpeg&w=3840&q=75)
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