00:01
For this problem, we are told that we have a bag of marbles where it is filled with three red marbles, two green marbles, one lavender, two yellow, and two orange.
00:09
And we are asked, how many sets of five marbles include at least two red ones, which is equivalent to saying how many sets have three red marbles or two red marbles? so in the case where we have three red marbles, we would have, well, there's only one way to fill those first three slots.
00:30
So we'd have one times the number of ways that we can fill the last two slots, which is going to be the number of combinations of, well, if we eliminate all three red marbles, it would be the number of combinations of seven items taken two at a time.
00:47
So we'd have one time seven choose two, which is going to equal 21.
00:52
Then if we have two marbles, or two red marbles, if we start off with taking, excellently deleted one of my red marbles, if we start off with taking the reds out, then how many choices for red would we have? well, we would have three choices taken two at a time, or the number of combinations of three items taken two at a time.
01:18
So that fills up our first two slots.
01:20
Then we need to fill up the other three slots...