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  • How many words, with or without meaning can be made from the letter of the word MIRACLE, assuming no letter is repeated if all letters are used at a time?<stro

How many words, with or without meaning can be made from the letter of the word MIRACLE, assuming no letter is repeated if all letters are used at a time?

Option: 1

 720


Option: 2

 5040


Option: 3

740

 


Option: 4

5020


Answers (1)

best_answer

The word MIRACLE has 7 different letters.

The words by using all the letters can be formed from the letters of the word MIRACLE, without the repetition of the letters, is the permutation of 7 different objects taken at a time is,

 ^7P_7 

Thus, the required number of ways to form a word by using all the letters is,

 ^7P_7=\frac{7!}{\left ( 7-7 \right )!} 

^6P_3=\frac{6!}{3!} 

^7P_7=7\times 6\times 5\times 4\times 3\times 2\times1 

^7P_7=5040  

Therefore, the number of ways to form a word is 5040 ways.

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