The number of ways in which the letters of the word PERSON can be placed in the squares of the given figure so that no row remains empty is

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$24 \times 6!$

$26 \times 6!$

$26 \times 7!$

$27 \times 6!$

answer is B.

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Detailed Solution

There are 6 different letters. We have to select 6 squares, taking at least one from each row and then arranging in each selection. Let us first select places in each row such that no row remains empty.

R₁	R₂	R₃	Number of selections
1	1	4	$^{2} {C_{1}}^{2} {C_{1}}^{4} C_{4} = 4$
1	2	3	$^{2} {C_{1}}^{2} {C_{2}}^{4} C_{3} = 8$
2	1	3	$^{2} {C_{2}}^{2} {C_{1}}^{4} C_{3} = 8$
2	2	2	$^{2} {C_{2}}^{2} {C_{2}}^{4} C_{2} = 6$

Therefore, the total number of selections of 6 squares is 4+ 8 + 8 + 6 = 26. For each selection of 6 squares, the number of arrangements of 6 letters is 6! = 720. Hence, the required number of ways is 26 x 720 = 18720.

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