How many words with or without meaning can be formed using all the letters of the word EQUATION , using each letter exactly once ?

Question

Answer

Total number of letters in the word equation=8,
number of ways=8P8,
=8!/(8-8)!,=8!=1×2×3×4×5×6×7×8=40320

Answer

《《 The number of words that can be formed using all the letters of the word EQUATION, using each letter exactly once, is the number of permutations of 8 different objects taken 8 at a time, which is 8P8=8!
Thus, required number of words that can be formed = 8! = 40320 》》

Answer

Introduction: In this question, we are required to form words using all the letters of the word 'EQUATION' such that each letter is used exactly once. In this answer, we will explore the various ways in which this can be done.

Method: To form words using all the letters of the word 'EQUATION' such that each letter is used exactly once, we can follow the following steps:

1. Find the number of letters in the word 'EQUATION' - There are 8 letters in the word 'EQUATION'.

2. Find the number of ways in which we can arrange these letters - The number of ways in which we can arrange 8 letters is 8! = 40,320.

3. Find the number of words that can be formed - Not all of these arrangements will form words. To form a word, we need to ensure that the letters are arranged in such a way that they make sense. Therefore, we need to remove all the arrangements that do not form words.

4. Find the number of meaningful words that can be formed - The word 'EQUATION' itself is a meaningful word. We can also form other meaningful words such as 'QUAINT', 'AQUINE', 'QUINATE', 'TOQUE', 'QUITE', 'TENIA', 'UNITE', 'QUOTA', 'INQUA', 'TUNA', 'NEAT', 'NOTE', 'TUNE', 'ANTI', 'AUNT', 'QUIT', 'UNIT', and 'EAT'.

5. Find the number of non-meaningful words that can be formed - There are many arrangements of letters that do not form meaningful words. For example, 'NITOEQA', 'UENTOQA', and 'QETUNOA' are not meaningful words.

Conclusion: Therefore, using all the letters of the word 'EQUATION' and each letter exactly once, we can form a total of 19 meaningful words and many non-meaningful words.

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