Question

Six Xs 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?

• A. $27$
• B. $28$
• C. $26$
• D. $35$

Answer 1

Answer: (C)

$26$

In all, we have $8$ squares in which six ${}^{\prime }{X}^{\prime }$ 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 possibilites are to be excluded. Hence, required number of ways $=28-2=26$