If all the words formed are arranged as in dictionary order, then what

1.	If all the words formed are arranged as in dictionary order, then what is the rank of word ‘COMPUTER’
Answer» Letters in word COMPUTER are C, O, M, P, U, T, E, R. ∴ Ascending order of letter in word COMPUTER according to dictionary order is C, E, M, O, P, R, T, U. C is fixed for smallest order in dictionary. Number of words starting with CE = 6! = 720, Number of words starting with CM = 6! = 720, Number of words starting with COE = 5! = 120, Number of words starting with COME = 4! = 24, Number of words starting with COMPE = 3! = 6, Number of words starting with COMPR = 3! = 6, Number of words starting with COMPT = 3! = 6, Number of words starting with COMPUE = 2! = 2, Number of words starting with COMPUR = 2! = 2, After these words, COMPUTER is next word. ∴ Rank of word COMPUTER = 720 + 720 + 120 + 24 + 6 + 6 + 6 + 2 + 2 + 1 = 1607.

If all the words formed are arranged as in dictionary order, then what is the rank of word ‘COMPUTER’

Answer»

Letters in word COMPUTER are C, O, M, P, U, T, E, R.

∴ Ascending order of letter in word COMPUTER according to dictionary order is C, E, M, O, P, R, T, U.

C is fixed for smallest order in dictionary.

Number of words starting with CE = 6! = 720,

Number of words starting with CM = 6! = 720,

Number of words starting with COE = 5! = 120,

Number of words starting with COME = 4! = 24,

Number of words starting with COMPE = 3! = 6,

Number of words starting with COMPR = 3! = 6,

Number of words starting with COMPT = 3! = 6,

Number of words starting with COMPUE = 2! = 2,

Number of words starting with COMPUR = 2! = 2,

After these words, COMPUTER is next word.

∴ Rank of word COMPUTER = 720 + 720 + 120 + 24 + 6 + 6 + 6 + 2 + 2 + 1 = 1607.

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