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All letters are used at a time.
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There are different letters in the word MONDAY.
The first place can be filled in ways.
Second place can be filled by any one of the remaining letters. So, second place can be filled in ways
Third place can be filled by any one of the remaining letters. So, third place can be filled in ways
So, on continuing, number of ways of filling fourth place in ways , fifth place in ways, six place in 1 way.
Therefore, the number of words that can be formed using all the letters of the word MONDAY, using each letter exactly once is
Alternative Method:
Number of words that can be formed by using all the letters of the word MONDAY at a time is the number of permutation of different objects taken at a time, which is
Thus, required number of words that can be formed when all letters are used at a time=
The first place can be filled in ways.
Second place can be filled by any one of the remaining letters. So, second place can be filled in ways
Third place can be filled by any one of the remaining letters. So, third place can be filled in ways
So, on continuing, number of ways of filling fourth place in ways , fifth place in ways, six place in 1 way.
Therefore, the number of words that can be formed using all the letters of the word MONDAY, using each letter exactly once is
Alternative Method:
Number of words that can be formed by using all the letters of the word MONDAY at a time is the number of permutation of different objects taken at a time, which is
Thus, required number of words that can be formed when all letters are used at a time=
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Question Text | All letters are used at a time. |
Answer Type | Text solution:1 |
Upvotes | 150 |