Question

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

• A. $24\times 6!$
• B. $26\times 6!$
• C. $26\times 7!$
• D. $27\times 7!$

Answer 1

The correct option is B $26\times 6!$

No of ways PERSON can be arranged = 6!
6 letters can be arranged in 8 letters
In ${}^8{C}_6$ ways.
${}^8{C}_6=\frac{8!}{2!6!}=\frac{8\times 7}{2!}=28$ways
Case 1: $R_1$ is empty \rightarrow 6 letters in 6 blocks in ${}^6{C}_6=1$ way.
Case 2: $R_2$ is empty \rightarrow 6 letters in 6 blocks in ${}^6{C}_6=1$ way.
Therefore no of row to be empty, no of arrangements
= $(28-1-1)6!$
= $26\times 6!$