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Expert: - 6/7/2010


Question
Five-digit sum. Find the sum of all five-digit numbers that are formed by using the digits 1, 2, 3, 4, and 5 once and only once.(with work shown)

Answer
There are 5!=120 differnt permutations of "12345" (i.e. 120 different5-digit numbers).
Each digit will appear in each position (i.e. units, tens, hundreds, thousands, and
ten-thousands) 1/5 of the time (i.e. 24 times).

Thus, the sum will be
24(11111)+24(22222)+24(33333)+24(44444)+5(55555)=24(11111+22222+33333+44444+55555)
=24(166665)=3999960

Abe

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Volunteer

Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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