Question 1161125
<font color=black size=3>
"At least 3" means "3 or more". Considering there are 4 red marbles, the only possible scenarios are:
<ul><li>picking exactly 3 red marbles</li><li>picking exactly 4 red marbles</li></ul>
--------------------------------------------


Let's consider the situation where we have exactly 3 red marbles selected. There are 4 red marbles overall, which means there are 4 ways to form a group of 3 selected red. Put another way, there are 4 ways to not a select a particular red marble. 


Using the combination function, you should find that *[Tex \Large _n C _r = 4] when n = 4 and r = 3.


There are 3 green marbles, 1 lavender, 3 yellows and 2 orange giving a total of 3+1+3+2 = 9 marbles that aren't red. Use the combination function to find *[Tex \Large _n C _r = 36] when n = 9 and r = 2. This says there are 36 ways to select two marbles from a pool of 9.


Multiply this with the number of ways to pick the red marbles (4) and we get 36*4 = 144


There are 144 ways to pick exactly 3 red marbles and 2 non-red marbles.


Let A = 144. We'll use it later.


--------------------------------------------


We have 4 red marbles. There is only one way to select a group of 4 red marbles if the pool size is also 4. 


There are 9 non-red marbles and only one slot to fill with this pool to pick from. So we have 9 different ways to fill it.


Overall, there are 1*9 = 9 different ways to pick four red marbles followed by one non-red marble.


Let B = 9


--------------------------------------------


The results from the earlier sections are then added up. The values of A and B can be added because the events they represent are mutually exclusive.


A+B = 144+9 = 153


Answer: <font color=red size=4>153</font>
</font>