Question

A bag contains two red marbles, three green ones, one lavender one, six yellows, and five orange marbles. HINT [See Example 7.] How many sets of four marbles include exactly two green marbles? (Note that this means there must be two other non-green marbles as well).

Answer 1

Answer:

sets are 273

Step-by-step explanation:

given data

red = 2

green = 3

lavender = 1

yellow = 6

orange = 5

solution

total no of marbles are = 2 + 3 + 1 + 6 + 5 = 17

so number of way selecting  four marbles include exactly two green marbles is

2 green and 2 others

non green are = 17 - 3 = 14

so c (3,2) × c(14,2)

= $\frac{3!}{1!*2!} * \frac{14!}{12!*2!}$

= 273

so sets are 273