Six $X$’s have to be placed in the square of the figure such that each row contains at least one ‘$X$’. In how many different ways can this be done? [image:7_image1.emf]

Question

Dr. Abubacker · Accepted Answer

(c)
In all, we have 8 squares in which 6 ‘$X$’ have to be placed and It can be done in $\ ^{8}C_{6} = 28$ ways.
But this includes the possibility that either the top or horizontal row does not have any ‘$X$’. Since, we want each row must have at least one ‘$X$’, these two possibilities are to be excluded.
Hence, required number of ways $= 28 - 2 = 26$

Q. Six $X$’s have to be placed in the square of the figure such that each row contains at least one ‘$X$’. In how many different ways can this be done?

Explanation

Reviewed by Dr. Abubacker

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