Question

Number of ways of arranging $5$ identical objects in the squares of given figure
in such a way that no row remains empty and one square can't have more then one object is

Answer 1

Following cases will be there:
We are given $5$ identical objects

Row No.	Case $1$	case $2$	case $3$	case $4$
$1^{st}$	$3$	$2$	$2$	$1$
$2^{nd}$	$1$	$2$	$1$	$2$
$3^{rd}$	$1$	$1$	$2$	$2$
No. of ways for each case	${}^4{C}_3{}^2{C}_1{}^2{C}_1$ $=16$	${}^4{C}_2{}^2{C}_2{}^2{C}_1$ $=12$	${}^4{C}_2{}^2{C}_1{}^2{C}_2$ $=12$	${}^4{C}_1{}^2{C}_2{}^2{C}_2$ $=4$

Hence, required number of ways
$=16+12+12+4$
$=44$