We have:.2) A bag of chips has 10 chips in it: 1 sour cream and onion,
2 BBQ, 3 regular, and 4 low fat chips.
I pick 5 chips at random.
There are possible outcomes.
We want 2 BBQ and 3 Others.(a) How many picks are there with at least 2 BBQ chips
There are:. picks.
I will assume this means: "at least 2 BBQ chips and at least 1 RG chip".(b) at least 2 BBQ chips and 1 regular chip
We want:.2BBQ, 1 RG, and 2 Others.
There are three possible cases.(c) all 4 chips represented
1 SC, 1 BBQ, 1 RG, 2 LF:.
1 SC, 1 BBQ, 2 RG, 1 LF:.
1 SC, 2 BBQ, 1 RG, 1 LF:.
There are: . ways.
The opposite of "at most 3" is "more than 3" (all 4 chips).(d) at most 3 chips represented
In part (c), we found that: .
I started reasoning out the possible cases, then came the dawn!(e) at least 2 chips represented
Think about it . . .
It is impossible to get five chips of the same type.
Hence, we will always get at least 2 types of chips.