Question

The number of numbers less than $1000$ that can be formed out of the digits $0,1,2,3,4$ and $5$, no digit being repeated, is:

• A. $130$
• B. $131$
• C. $156$
• D. none of these

Answer 1

The correct option is B $131$

Given that no. of numbers less than $1000$ that can be formed out of the digits $0,1,2,3,4$ & $5$

$\left(1\right)$ $3$ digit numbers

Chooses the frist digit any of $5$ ways

(It can't be $0$)

Choose the second digit any of $5$ ways

(It can be $0$)

Choose the third digit any of $4$ ways

i.e., $\left(5\right)\left(5\right)\left(4\right)=25\times 4$

$=100$

$\left(2\right)$ $2$ digit numbers

Choose the first digit any of $5$ ways

(It can't be $0$)

Choose the second digit any of $5$ ways

(It can be $0$)

i.e., $5\times 5=25$

$\therefore$ It is $2$ digit number

$\left(3\right)$ $1$-digit numbers: There are only of

$6$ ways $0,1,2,3,4,5=6$

$\therefore$ Total$=100+25+6=131$.