Each of the integers from 1 to 16 is written on the a seperate index card and placed in a box.
Each of the integers from 1 to 16 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?
Answer/Solution
9
Steps/Work
Out of the 16 integers: 8 are odd and 8 are even.
If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:
1. we will end up picking odd numbers one by one, so we will pick all 8 odd numbers first
2. 9th number will be the first even number
So we need to withdraw at least 9 numbers to make sure that we get one even number and the product of all the integers picked is even.
So, answer will be 9. (A)
If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:
1. we will end up picking odd numbers one by one, so we will pick all 8 odd numbers first
2. 9th number will be the first even number
So we need to withdraw at least 9 numbers to make sure that we get one even number and the product of all the integers picked is even.
So, answer will be 9. (A)