How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

C₁ | C₂

(a)   4 letters are used at a time |                                                   (i) 720

(b)   All letters are used at a time | (ii) 240

(c)   All letters are used but the first is a vowel | (iii) 360

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Payal Gupta | Contributor-Level 10

3 months ago

This is a matching answer type question as classified in NCERT Exemplar

$\begin{array}{l} (a) 4 l e t t e r s a r e u s e d a t a t i m e = {}_{6}{P_{4}} = \frac{6!}{2!} = 360 \\ (b) A l l l e t t e r s a r e u s e d a t a t i m e = {}_{6}{P_{6}} = 6! = 720 \\ (c) A l l l e t t e r s a r e u s e d b u t f i r s t l e t t e r i s v o w e l = 2 \times 5! = 2 \times 120 = 240 \\ H e n c e, t h e r e q u i r e d m a t c h i n g i s \\ (a) \leftrightarrow (i i i), (b) \leftrightarrow (i), (c) \leftrightarrow (i i) \end{array}$

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How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if C1 | C2 (a) 4 letters are used at a time | (i) 720 (b) All letters are used at a time | (ii) 240 (c) All letters are used but the first is a vowel | (iii) 360