Question

Six X's have to be placed in the square of given figure such that each row contains at least one X. Then number of ways doing so are

• A. 28
• B. 26
• C. 6!
• D. 8! . 6!

Answer 1

Answer: (B)

26

In the above problem all the $X^{\prime }s$ are identical, hence selection of 6 squares of 8 rows can be done in the following ways

$R_1$	$R_2$	$R_3$
1	4	1	${}^2{C}_1.{}^4{C}_4{}^2{C}_1=4$
1	3	2	${}^2{C}_1.{}^4{C}_3{}^2{C}_2=8$
2	3	1	${}^2{C}_2.{}^4{C}_3{}^2{C}_1=8$
2	2	2	${}^2{C}_2.{}^4{C}_2{}^2{C}_2=6$

Hence total number of ways is
$4+8+8+6$
$=26$