+1206 Five balls are numbered with the integers 1 through 5 and placed in a jar. Three are drawn without replacement. What is the probability that the sum of the three integers on the balls is odd? Express your answer as a common fraction.
+6248 The balls can sum to odd if they are
(o, o, o), (o, e, e)
There is only 1 way to choose (o,o,o), i.e. (1,3,5)
There are 3 ways to choose (o,e,e), both the two even numbers, 2 and 4, and one of the odd numbers.
Thus there are 4 total ways 3 balls can sum to an odd number.
There are \(\dbinom{5}{3} = 10\) total ways to select 3 balls from the 5. Thus
\(P[\text{choose 3 balls that sum to an odd number}]=\dfrac{4}{10}=\dfrac 2 5\)
+6248 The balls can sum to odd if they are
(o, o, o), (o, e, e)
There is only 1 way to choose (o,o,o), i.e. (1,3,5)
There are 3 ways to choose (o,e,e), both the two even numbers, 2 and 4, and one of the odd numbers.
Thus there are 4 total ways 3 balls can sum to an odd number.
There are \(\dbinom{5}{3} = 10\) total ways to select 3 balls from the 5. Thus
\(P[\text{choose 3 balls that sum to an odd number}]=\dfrac{4}{10}=\dfrac 2 5\)
