Question

A five digit number is formed satisfying the following conditions: (i) sum of digits is 8 (ii) digits used are 1, 2 & 3, and (iii) the number is divisible by 4. Then number of such numbers formed is equal to ___

Answer 1

5- digit no. is formed using digits 1,2 and 3
If number is divisible by 4, then last 2 digits should be divisible by 4
$\underset{–}{}\underset{–}{}\underset{–}{}\underset{–}{1}\underset{–}{2}$
$\underset{–}{}\underset{–}{}\underset{–}{}\underset{–}{3}\underset{–}{2}$
Number having 12 as last 2 digits and sum of digits 8
$=311\underset{–}{12}=\frac{3!}{2!}=3$
$=221\underset{–}{12}=\frac{3!}{2!}=3$
Numbers having 32 as last 2 digits and sum of digits 8
$=111\underset{–}{32}=\frac{3!}{3!}=1$
$\therefore$ Total numbers formed $=3+3+1$
$=7$