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in Combinatorics and Mathematical Induction by (46.9k points)
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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 II III IV V VI

(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?

1 Answer

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Best answer

The word MONDAY has 6 distinct letters.

(i) 4 letters out of 6 can be arranged in 6P4 ways. 

∴ The required number of words = 6P4 = 6 × 5 × 4 × 3 = 360

(ii) 6 letters can be arranged among themselves in 6P6 ways. 

∴ The required number of words = 6P6 = 6! 

= 1 × 2 × 3 × 4 × 5 × 6 = 720.

(iii) The first place can be filled by anyone Of the two vowels O or A in 2 ways. The remaining 5 letters can be arranged in the remaining 5 places II to VI in 5P5 = 5! ways. 

∴ By the multiplication rule, the required number of words = 2 × 5! = 2 × 1 × 2 × 3 × 4 × 5 = 240

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