Question

Number of $5$ digited numbers using $0,1,2,3,4,5$ divisible by $5$ repetition is allowed

• A. $216$
• B. $100$
• C. $140$
• D. $180$

Answer 1

The correct option is A $216$

we have,

$0,1,2,3,4,5$

$\begin{array}{c}\overline{\downarrow }\\ {}^4{C}_1\end{array}\begin{array}{c}\overline{\downarrow }\\ {}^4{C}_1\end{array}\begin{array}{c}\overline{\downarrow }\\ {}^3{C}_1\end{array}\begin{array}{c}\overline{\downarrow }\\ {}^2{C}_1\end{array}\begin{array}{c}\overline{\downarrow }\\ {}^1{C}_1\end{array}$

$=5\times 4\times 3\times 2\times 1$

$=120$

when unit digit 5

$\begin{array}{c}\overline{\downarrow }\\ {}^5{C}_1\end{array}\begin{array}{c}\overline{\downarrow }\\ {}^4{C}_1\end{array}\begin{array}{c}\overline{\downarrow }\\ {}^3{C}_1\end{array}\begin{array}{c}\overline{\downarrow }\\ {}^2{C}_1\end{array}\begin{array}{c}\overline{\downarrow }\\ {}^1{C}_1\end{array}$

$=4c_1\times 4c_1\times 3c_1\times 2c_1\times 1$

$=96$

Total 5 digit No=

$=120+96$

$=216$

Hence this is the answer