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

sets are 273

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)

=
`(3!)/(1!*2!) * (14!)/(12!*2!)`

= 273

so sets are 273