Respuesta :
Answer:
There are 12 sets of four marbles include all the red ones.
Step-by-step explanation:
Given : A bag contains three red marbles, two green ones, one lavender one, four yellows, and five orange marbles.
To find : How many sets of four marbles include all the red ones?
Solution :
Number of red marbles = 3
Number of green marbles = 2
Number of lavender marbles = 1
Number of yellow marbles = 4
Number of orange marbles = 5
We have to form sets of four marbles include all the red ones,
For position of getting red ones we have three red marbles i.e. [tex]^3C_3[/tex]
For the fourth one we have 12 choices i.e. [tex]^{12}C_1[/tex]
Total sets of four marbles include all the red ones is
[tex]=^3C_3\times ^{12}C_1[/tex]
[tex]=1\times 12[/tex]
[tex]=12[/tex]
Therefore, There are 12 sets of four marbles include all the red ones.
