NCERT Class XI Mathematics - Permutations and Combinations - Solutions
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Question : 19
Total: 41
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
Solution:
No. of letters in the word MONDAY = 6
(i) When 4 letters are used at a time.
Then, the required number of words =
P 4
(ii) When all letters are used at a time. Then the required number of words =
P 6
(iii) All letters are used but first letter is a vowel.
So the first letter can be either A or O. So there are 2 ways to fill the first letter & remaining places can be filled in
P 5
∴ The required number of words = 2 ×
P 5
(i) When 4 letters are used at a time.
Then, the required number of words =
(ii) When all letters are used at a time. Then the required number of words =
(iii) All letters are used but first letter is a vowel.
So the first letter can be either A or O. So there are 2 ways to fill the first letter & remaining places can be filled in
∴ The required number of words = 2 ×
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