Question

If the letters of the word MASTER are permitted in all possible ways and the words thus formed are arranged in the dictionary order, then find the rank of the word MASTER.

Answer 1

Solution:

The alphabetical order of the letters of the given word is $A,E,M,S,R,T.$

The number of words begin with $A$ is $5!=120.$

The number of words begin with $E$ is $5!=120.$

The number of words begin with $MAE$ is $3!=6.$

The number of words begin with $MAR$ is $3!=6.$

The number of words begin with $MASE$ is $2!=2.$

The number of words begin with $MASR$ is $2!=2.$

The next word is $MASTER.$

$\therefore$ Rank of the word $MASTER=2\left(120\right)+2\left(6\right)+2\left(2\right)+1$

$=240+12+4+1$

$=257.$