2002 AMC 10B Problem 9

Using the letters

A,

M,

O,

S,

and

U,

we can form

120

five-letter “words.” If these “words” are arranged in alphabetical order, then the “word”

USAMO

occupies which position?

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Solution

The alphabetical order of the letters is

A, M, O, S, U.

Words beginning with

A,

M,

O,

S

fill positions

1

through

96

(four choices of first letter,

24

each). Words beginning with

U

occupy positions

97

–

120.

Listing them alphabetically,

USAMO

is the

19

th such word, so it occupies position

96 + 19 = 115.

Thus, the correct answer is D.