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Question
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel?
Solution
There are six letters in the word MONDAY.
All the letters are used, but the first letter is a vowel:
There are two vowels, namely A and O, in the word MONDAY.
For the first letter, out of the two vowels, one vowel can be chosen in 2C1 ways.
The remaining five letters can be chosen in 5C5 ways.
So, the letters in 5C5 group can be arranged in \[5!\]ways.
∴ Number of ways =\[{}^2 C_1 \times^5 C_5 \times 5! = 2 \times 1 \times 5! = 240\]
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