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## Sum equal to 5

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rajatvmittal Really wants to Beat The GMAT!
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Sum equal to 5 Mon Mar 12, 2012 8:26 am
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• Lap #[LAPCOUNT] ([LAPTIME])
How many positive integers less than 10,000 are there in which sum of digits equals 5?

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Mon Mar 12, 2012 9:47 am
that means a four digit number whose digits should sum up to 5:-
number containing: 2,1,1,1 => 4 such numbers
2,2,1,0 => 12 such numbers
3,1,1,0 => 12 such numbers
3,2,0,0 => 12 such numbers
4,1,0,0 => 12 such numbers
5,0,0,0 => 4 such numbers
thus total of 4+12+12+12+12+4 = 56 numbers with sun of digit =5 and number < 10,000[/u]

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Mon Mar 12, 2012 9:31 pm
rajatvmittal wrote:
How many positive integers less than 10,000 are there in which sum of digits equals 5?
We need to find integers between 0 to 9999, in which the sum of digits adds up to 5.

(1) One digit is 5 and all other are 0: 0005, 0050, 0500, 5000 or we can say that no. of ways we can arrange the digits = 4!/3! = 4 ways
(2) Three 1's and one 2: 1112, this can be done in 4!/3! = 4 ways
(3) One 4 and one 1: 4100, this can be done in 4!/2! = 12 ways
(4) One 3 and one 2: 3200, this can be done in 4!/2! = 12 ways
(5) One 3 and two 1's: 3110, this can be done in 4!/2! = 12 ways
(6) Two 2's and One 1: 2210, this can be done in 4!/2! = 12 ways

Therefore, required number of positive integers = (12 * 4) + (4 * 2) = 48 + 8 = 56

The correct answer is C.

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