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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

\begin{array}{|l|l|l|l|} \hline \mathbf{C}_{\mathbf{1}} & & \mathbf{C}_{2} & \\ \hline \text { (a) } & \begin{array}{l} \text { 4 letters are used } \\ \text { at a time } \end{array} & \text { (i) } & 720 \\ \hline \text { (b) } & \begin{array}{l} \text { All letters are } \\ \text { used at a time } \end{array} & \text { (ii) } & 240 \\ \hline \text { (c) } & \begin{array}{l} \text { All letters are } \\ \text { used but the first } \\ \text { is a vowel } \end{array} & \text { (iii) } & 360 \\ \hline \end{array}

Answers (1)

Given that Total number of letter of MONDAY=6 

Total vowel=2

 a. When 4 letters are used at a time=  ^6P_4=360

 b. All the letters are used at a time =  ^6P_6=720

 c. All letters are used but the first is a vowel=2. 5!

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