Six 'X's have to be placed in the squares of | vedclass

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(C) The figure consists of $8$ squares arranged in $4$ horizontal rows: the top row has $2$ squares,the second row has $4$ squares,the third row has $

Vedclass · Accepted Answer

$26$

Vedclass · Answer

(C) The figure consists of $8$ squares arranged in $4$ horizontal rows: the top row has $2$ squares,the second row has $4$ squares,the third row has $4$ squares,and the bottom row has $2$ squares. Wait,looking at the figure,it is a $4 	imes 4$ grid structure with corners removed. Specifically,there are $2$ squares in the top row,$4$ in the second,$4$ in the third,and $2$ in the bottom row. Total squares = $12$. Let's re-examine the figure: it is a cross shape. The top row has $2$ squares,the middle two rows have $4$ squares each,and the bottom row has $2$ squares. Total squares = $2 + 4 + 4 + 2 = 12$. Actually,the figure shows a $2 	imes 2$ central block with $1$ square attached to each side,totaling $8$ squares. Row $1$ (top): $2$ squares.Row $2$ (middle): $4$ squares.Row $3$ (middle): $4$ squares.Row $4$ (bottom): $2$ squares.Total squares = $12$. Re-reading the problem: "Six '$X$'s have to be placed in the squares of the figure such that each row contains at least one '$X$'." Total ways to place $6$ '$X$'s in $8$ squares is $^8C_6 = 28$. If the figure is $8$ squares total,the rows are: Top ($2$ squares),Middle ($4$ squares),Bottom ($2$ squares). Total ways = $^8C_6 = 28$. Cases to exclude: $1$. Top row empty: We must place $6$ '$X$'s in the remaining $6$ squares. This can be done in $^6C_6 = 1$ way. $2$. Bottom row empty: We must place $6$ '$X$'s in the remaining $6$ squares. This can be done in $^6C_6 = 1$ way. Total valid ways = $28 - 1 - 1 = 26$.

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

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