Question

Number of $4$ digit numbers of the form
$N=abcd,$ which satisfy following conditions :
$\left(i\right)4000\le N<6000$
$\left(ii\right)N$ is a multiple of $5$
$\left(iii\right)3\le b<c\le 6$ is equal to

• A. $16$
• B. $12$
• C. $4$
• D. $24$

Answer 1

The correct option is D $24$

We have $N=abcd$
First place a can be filled in $2$ ways i.e.$4,5$ (as $4000\le N<6000$ )

For $b$ and $c,$ total $6$ possibilities are there i.e. $34,35,36,45,46,56$
(as $3\le b<c\le 6$ )

Last place $d$ can be filled in $2$ ways i.e. $0,5$ (as $N$ is a multiple of $5$)

Hence, total possible numbers $=2\times 6\times 2=24$