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in Mathematics by (52.5k points)

How many letters words with or with out 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?

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Best answer

There are 6 letters in the word MONDAY. So, the total number of words is equal to the number of arrangements of these letters taken four at a time. 

The number of such arrangements = 6P4 = 6/(6 - 4) = 6/2 = (6 x 5 x 4 x 3 x 2 x 1)/(2 x 1) = 360

Hence, total number of words = 360 

(ii) Total number of arrangements in this case = 6P6 = 6! = 720 

(iii) Total number of arrangements when all letters are used but the first letter is a vowel 

= 2 × 5P5 = 2 × 5! = 2 × 5 × 4 × 3 × 2 × 1 = 240.

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