Question
Match each item given under the column $C_1$ to its correct answer given under the column $C_2.$
How many words $($with or without dictionary meaning$)$ can be made from the letters of the word $\text{MONDAY,}$ assuming that no letter is repeated$,$ if
 
$C_1$
 
$C_2$
$(a)$
$4$ 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.
$(iii)$ $360$

Answer

 
$C_1$
 
$C_2$
$(a)$
$4$ letters are used at a time.
$(iii)$ $360$
$(b)$
All letters are used at a time.
$(i)$ $720$
$(c)$
All letters are used but the first is a vowel.
$(ii)$ $240$
  1. $4$ Letter are used at time $=\ ^6\text{P}_4=\frac{6!}{2!}=360$
  2. All letters are used at time $^6\text{P}_6=6!=720$
  3. All letters are used but first letter is vowel $=2\times5!=2\times120=240$

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