Question

I : The number of five digit numbers that can be formed with $0,1,2,3,5$ which are divisible by $5$ is $18$.
II : The sum of all four digit numbers that can be formed with $1,2,3,4$ so that no digit being repeated in any number is $66660$.
Which of the above statements is true?

• A. only I
• B. only II
• C. Both I and II
• D. Neither I nor II

Answer 1

Answer: (B)

only II

Case I: $\Rightarrow$ last digit $=0$
$C_I=4!=24$
Case II $\Rightarrow$ Last digit $=5$
$C_{II}=3\times 3!=18$
$S=C_I+C_{II}=42$
II $\Rightarrow$ Sum here is
$S=3!\times [1+2+3+4]\times [{10}^0+{10}^1+{10}^2+{10}^3]$
$=6\times 10\times \left[1111\right]$
$=60\times 1111$
$S=66660$