How many letters words with or with out meaning can be made from the l

1.	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?
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.

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?

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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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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