Question

The letters of the word MASTER are permuted in all possible ways and the words thus formed are arranged as in a dictionary. The rank of the word STREAM is

• A. $597$
• B. $480$
• C. $612$
• D. $385$

Answer 1

The correct option is A $597$

The alphabetical order of the letters of the given word is A, E, M, R, S, 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 M is $5!=120$
The number of words begin with R is $5!=120$
The number of words begin with SA is $4!=24$
The number of words begin with SE is $4!=24$
The number of words begin with SM is $4!=24$
The number of words begin with SR is $4!=24$
The number of words begin with STA is $3!=6$
The number of words begin with STE is $3!=6$
The number of words begin with STM is $3!=6$
The number of words begin with STRA is $2!=2$
Next word is STREAM
Rank is $120+120+120+120+24+24+24+24+6+6+6+2+1=597$.