Question

The different number of ways the letters of the word ${}^{\prime }YOGES{H}^{\prime }$ can be placed in the 8 boxes of the given figure so that no row remains empty is

• A. $26\times 7!$
• B. $26\times 6!$
• C. $26\times 5!$
• D. $26\times 4!$

Answer 1

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

The total number of ways in which the rows can be filled ${=}^8{C}_6=28$ ways
Out of these there will be two cases in which a row will be empty: the case where the top row is empty and the case where the bottom row is empty.
So, the ways in which no row is empty $=28-2$ $=26$
YOGESH can be arranged in $6$ selected places in $6!$ ways
So, the total number of ways of placing $=26\times 6!$
Hence, option 'B' is correct.