Question
Match each item given under the column $C_1$ to its correct answer given under the column $C_2.$
Using the digits $1, 2, 3, 4, 5, 6, 7,$ a number of $4$ different digits is formed. Find
 
$C_1$
  $C_2$
$(a)$
how many numbers are formed.
$(i)$ $840$
$(b)$
how many numbers are exactly divisible by $2.$
$(ii)$ $200$
$(c)$
how many numbers are exactly divisible by $25.$
$(iii)$ $360$
$(d)$
how many of these are exactly divisble by $4.$
$(iv)$ $40$

Answer

 
$C_1$
  $C_2$
$(a)$
how many numbers are formed.
$(i)$ $840$
$(b)$
how many numbers are exactly divisible by $2.$
$(iii)$ $360$
$(c)$
how many numbers are exactly divisible by $25.$
$(iv)$ $40$
$(d)$
how many of these are exactly divisble by $4.$
$(ii)$ $200$
  1. Total of $4$ digit number formed with $ 1, 2, 3, 4, 5, 6, 7 =\ ^7\text{P}_4=\frac{7!}{(7-4)!}=\frac{7\times6\times5\times4\times3!}{3!}=840$
  2. When anumber is divisible by $2=4\times5\times6\times3=360$
  3. Total number which are divisible by $25 = 40$
  4. Total number which are divisible by $4\  ($last two digits is divisible by $4) = 200$

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