Question

If the letters of the word ‘MOTHER’ be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the ‘MOTHER’ is

Answer 1

Apply permutations to obtain the required answer

The alphabetical order of the given word ‘MOTHER’ is E, H, M, O, R, T.

The number of words starting with ‘E’ is $5!=120$.

The number of words starting with ‘H’ is $5!=120$.

The number of words starting with ‘ME’ is $4!=24$.

The number of words starting with ‘MH’ is $4!=24$.

The number of words starting with ‘MOE’ is $3!=6$.

The number of words starting with ‘MOH’ is $3!=6$.

The number of words starting with ‘MOR’ is $3!=6$.

The number of words starting with ‘MOTE’ is $2!=2$.

The number of words starting with ‘MOTHER’ is $1$.

Thus the position of the word ‘MOTHER’ is $\left(120+120+24+24+6+6+6+2+1\right)=309$.

Hence, the position of the ‘MOTHER’ is $309$.