The letters of the word ‘RANDOM’ are arranged as in a dictionary. What is the rank of word ‘RANDOM’?

Solution

Numbers of letters in 'RANDOM' = (R → 1, A → 1, N → 1, D → 1, O → 1, M → 1) = 6
Number of words that begin with A = $straight P presuperscript 1 subscript 1 cross times 5 factorial space equals space 1 cross times 120 space equals space 120$
Number of words that begin with D = $straight P presuperscript 1 subscript 1 cross times 5 factorial space equals space 1 space cross times space 120 space equals space 120$
Number of words that begin with M = $straight P presuperscript 1 subscript 1 cross times 5 factorial space equals space 1 cross times 120 equals 120$
Number of words that begin with O = $straight P presuperscript 1 subscript 1 cross times 5 factorial space equals space 1 cross times 120 equals 120$
Number of words that begin with N = $straight P presuperscript 1 subscript 1 cross times 5 factorial space equals space 1 cross times 120 equals 120$
So far, we have formed 120 + 120 + 120 + 120 + 120 = 600 words.
Now words starting with R.
Number of words starting with RAD = 1 x 1 x 1 x 3! = 6.
Number of words starting with RAM = 1 x 1 x 1 x 3! = 6.
Total words = 600 + 12 = 612.
613th word is RANDMO
614th word is RANDOM
∴ Rank of the word random in a dictionary is 614.

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Permutations And Combinations

The letters of the word ‘RANDOM’ are arranged as in a dictionary. What is the rank of word ‘RANDOM’?

Some More Questions From Permutations and Combinations Chapter

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.

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