The question is:
How many ways can you arrange six $X$s in the given figure so that each row has at least one $X$?
(Image taken from the same question from Math Exchange.)
My solution: To have $3$ $X$s in $3$ rows, there are $2 \cdot 4 \cdot 2$ ways to place them. Now there remain $5$ places more and we have $3$ $X$s remaining. So to fill the remaining places, there are $C^5_3$ ways. So total number of ways $= 16 \cdot 10 = 160$. But the answer is $26$. Where am I wrong? Thank you.