Question

If the letters of the word ‘RANDOM’ are arranged alphabetically as in a dictionary, what will be the 611thword?

Answer 1

Answer:

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Answer 2

ANSWER

Arranging RANDOM in dictionary order gives us

ADMNOR.

Consider the words starting with A. If the starting letter is fixed as A, then the remaining 5 letters can be rearranged in 5! ways.

Similarly with the words starting with letters D,M,N,O.

Hence 5×5!

=5(120)

=600 ...(i)

Now consider the words starting with R,

R−−−−−

In Dictionary order the first word starting with R will be

RADMNO

Keeping the positions of RAD fixed we can rearrange the letters MNO in 3! ways.

Similarly for RAMDNO.

Hence

600+2(3!)

=612.

The successive word will be

RANDMO and RANDOM.

Hence the rank of the word RANDOM is 612+2=614

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