Question

1.A bag contains 5​blue, 4​ red, and 3green marbles. Four marbles are drawn at random from the bag. How many different samples are possible which include exactly two red​ marbles?

2.A bag contains 5 ​blue, 3 ​red, and 4 green marbles. Four marbles are drawn at random from the bag. How many different samples are possible which include at least one marble of each​ color

Answer 1

1. There must two red marbles out of four marbles.

So, the possible combinations would be:

i) 2 red, 1 blue and 1 green

ii) 2 red and 2 blue

iii) 2 red and 2 green

Hence, assuming the marbles of same colors are identical, three different samples are possible. (Ans).

2. There must be at least one marble of each color out of 4 marbles.

So, the possible combinations would be:

i) 2 red, 1 blue and 1 green

ii) 1 red, 2 blue and 1 green

iii) 1 red 1 blue and 2 green

So, assuming the marble of same colors are identical, 3 different samples are possible. (Ans).