# Probability Discrete Math. {1,2,3,4,5,6,7,8,9} What is the probability that the sum of any of these three numbers is odd?

Probability Discrete Math
{1,2,3,4,5,6,7,8,9} What is the probability that the sum of any of these three numbers is odd?
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Step 1
Three numbers can be choosen out of 9 in $\left(\genfrac{}{}{0}{}{9}{3}\right)$ possible ways.
Step 2
The sum will be odd if the three numbers are choosen either from {1,3,5,7,9} which can be done in $\left(\genfrac{}{}{0}{}{5}{3}\right)$ ways or one number is choosen from {1,3,5,7,9} - $\left(\genfrac{}{}{0}{}{5}{1}\right)$ ways and 2 numbers are choosen from {2,4,6,8} which can be done in $\left(\genfrac{}{}{0}{}{4}{2}\right)$ ways. So the cases when the sum is odd are $\left(\genfrac{}{}{0}{}{5}{3}\right)+\left(\genfrac{}{}{0}{}{5}{1}\right)×\left(\genfrac{}{}{0}{}{4}{2}\right)$.