Six X have to be placed in the squares of Figure such that each row contain at least one X. The number of ways in which this can be done is

Question

Six X have to be placed in the squares of Figure such that each row contain at least one X. The number of ways in which this can be done is (A) 25 (B) 26 (C) 27 (D) 30

Tardigrade Admin · Accepted Answer

This can be done in four mutually exclusive ways as follows:

	Row $R_{1}$	Row $R_{2}$	Row $R_{3}$	Number of ways
I	1	3	2	$(^{2} C_{1}) (^{4} C_{3}) (^{2} C_{2}) = 8$
II	1	4	1	$(^{2} C_{1}) (^{4} C_{4}) (^{2} C_{1}) = 4$
III	2	2	2	$(^{2} C_{2}) (^{4} C_{2}) (^{2} C_{2}) = 6$
IV	2	3	1	$(^{2} C_{2}) (^{4} C_{3}) (^{2} C_{1}) = 8$
			Total	26

Q. Six X have to be placed in the squares of Figure such that each row contain at least one X. The number of ways in which this can be done is

25

26

27

30

This can be done in four mutually exclusive ways as follows: Row R1​ Row R2​ Row R3​ Number of ways I 1 3 2 (2C1​)(4C3​)(2C2​)=8 II 1 4 1 (2C1​)(4C4​)(2C1​)=4 III 2 2 2 (2C2​)(4C2​)(2C2​)=6 IV 2 3 1 (2C2​)(4C3​)(2C1​)=8 Total 26

Q. Six $X$ have to be placed in the squares of Figure such that each row contain at least one $X$ . The number of ways in which this can be done is