# Word Formed By Rearranging The Letters Of Another

**Word Formed By Rearranging The Letters Of Another** – E.g. 7.3, 9 How many words, with or without meaning, can be made from the letters of the word MONDAY, assuming that no letter is repeated if 4 letters are used at the same time, The total number of alphabets of MONDAY = 6, so n = 6 If 4 letters are used at the same time, r = 4 Number of different words = nPr = 6P4 = (6! )/(6 − 4)! = 6!/2! = (6 × 5 × 4 × 3 × 2!)/2! = 6 × 5 × 4 × 3 = 360 7.3. example, 9 How many meaningful or meaningless words can be made from the letters of the word MONDAY, assuming that no letter is repeated, if (ii) all the letters are used at one time, Total number of alphabets of MONDAY = 6 Hence n = 6 If all letters are used at once , r = 6 Number of different words = nPr = 6P6 = (6! )/(6 − 6)! = 6!/0! = 6!/1 = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 Example 7.3, 9 How many words, with or without meaning, can be made from the letters of the word MONDAY, assuming that no letter is repeated, if (iii) all letters are used but the first letter vowel? The first letter must be a vowel (a, e, i, o, u) The vowels in MONDAY are O and A Assuming the first letter is O If the first letter is O, then the word will have the following form: Number of letters left = 5 n = 5 Number Number of letters to be used = 5 r = 5 Number of different words = 5P5 = 5!/(5 − 5)! = 5!/0! = 5!/1 = 5! = 5 × 4 × 3 × 2 × 1 = 120 Similarly, if the first letter is A , the number of different words = 120 So the number of words required = 120 + 120 = 240

Davneet Singh completed his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching for 12 years. He holds courses in mathematics, natural science, social science, physics, chemistry, and computer technology at the address.

## Word Formed By Rearranging The Letters Of Another

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