Question

A bag contains three red marbles, two green ones, one lavender one, four yellows, and five orange marbles. HINT [See Example 7. How many sets of four marbles include all the red ones?

Answer 1

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. $^3C_3$

For the fourth one we have 12 choices i.e. $^{12}C_1$

Total sets of four marbles include all the red ones is

$=^3C_3\times ^{12}C_1$

$=1\times 12$

$=12$

Therefore, There are 12 sets of four marbles include all the red ones.