Why arrangement is required for the case of even + even + odd
Three number from 1 to 100 (inclusive ) are selected at random and the numbers can be repeated. What is the probability that the sum of the three numbers will be odd?
For case Even +even + odd : why do we need to consider the arrangement of the numbers? The question is related to the sum and it does not matter which number you pick first.
The possible arrangements can be
Odd + Odd + Odd
Even + Even + Odd
The 2nd one can have many forms like E,E,O or E,O,E or O,E,E therefore we need to consider arrangements as well because they all are distinct.
Thus the probability will be:
50/100 x 50/100 x 50/100 for Odd + Odd + Odd.
50/100 x 50/100 x 50/100 x 3!/2! for Even + Odd + Odd all permutations.
1/8 + 1/8 x 3 = 4/8 = 1/2 Answer
