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Probability Level 3

How many three digit numbers are there whose sum of the digits is odd?


The answer is 450.

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Naitik Sanghavi by naitik sanghavi , 20, India

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3 solutions

Akhil Bansal
Jul 24, 2015

Let xyz be the number whose sum of digits is odd.
There are 4 possible case possible.
1) x is even ,y is even and z is odd = 4 × 5 × 5 4\times5\times5 = 100 ways.
2) x is even ,y is odd and z is even = 4 × 5 × 5 4\times5\times5 = 100 ways.
3) x is odd , y is even and z is even = 5 × 5 × 5 5\times5\times5 = 125 ways.
4) x is odd ,y is odd , z is odd = 5 × 5 × 5 5\times5\times5 = 125 ways.
Hence,add result of above cases,we get total 450 \boxed{450} ways.


5 Helpful 0 Interesting 0 Brilliant 0 Confused

Akhil, Can you please explain how we find the number of ways for each of the possibilities. (I didn't understand these steps: 4 × 5 × 5 4\times5\times5 =100 ways... )

Vignesh Rao - 5 years, 5 months ago

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For this, you have to understand rule of product

Akhil Bansal - 5 years, 5 months ago

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Ok Thank You.

Vignesh Rao - 5 years, 5 months ago
Cleres Cupertino
Aug 21, 2015

There are 900 three digit numbers. The half of them the sum is odd and the other half is even.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

I seriously like this solution of yours Cleres.

Vignesh Rao - 5 years, 5 months ago 
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def sum_of_digits(n):
    ans = 0
    while n:
        ans += (n%10)
        n /= 10
    return ans    

ctr = 0
for n in range(100, 1000):
    if sum_of_digits(n) % 2 != 0:
        ctr += 1

print ctr

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