Question

Consider a bag containing four red marbles, three green ones, one transparent one, three yellow ones, and three orange ones.

How many possible sets of five marbles are there in which none of them are red or green?

Answer 1

Answer: 21

Explanation:

Given : Number of red marbles = 4

Number of green marbles =3

Number of transparent marbles =1

Number of yellow marbles =3

Number of orange marbles =3

If we want to count the sets of five marbles are there in which none of them are red or green, the we exclude green and red marbles from the total marbles.

i.e. Total required marbles = 1+3+3=7

Now, the number of possible sets of five marbles are there:-

`^7C_5=(7!)/(5!(7-5)!)=(7*6*5!)/(5!2!)=21`

Hence, the number of possible sets of five marbles =21