A bag contains 2 red marbles, 4 green ones, 1 lavender one, 2 yellows, and 6 orange marbles. How many sets of four marbles include all the red ones?
To find the number of sets of four marbles that include all the red ones, we first need to determine the total number of marbles in the bag.
The bag contains:
- 2 red marbles
- 4 green marbles
- 1 lavender marble
- 2 yellow marbles
- 6 orange marbles
Total number of marbles = 2 + 4 + 1 + 2 + 6 = 15 marbles
Since we want to include all the red marbles, we already have 2 red marbles in every set. So, we need to choose 2 more marbles out of the remaining 13 marbles in the bag.
To find the number of sets, we can use combinations, denoted by "C(n, r)" or "nCr," which gives the number of ways to choose r items from a group of n items without considering the order.
In this case, we need to calculate "C(13, 2)."
C(13, 2) = 13! / (2!(13-2)!)
= (13 * 12) / (2 * 1)
= 78
Therefore, there are 78 sets of four marbles that include all the red ones.