Question

A bag contains three red marbles, three green ones, one lavender one, one How many sets of five marbles include at least two red ones?

Answer 1

Answer with Step-by-step explanation:

The number of marbles are as under

3 red , 3 green , 1 Lavender total = 7

Now to select five marbles from a total of 7 marbles such that at least 2 marbles are included are the sum of the following cases:

1) We select 2 exactly 2 red marbles from 3 reds and the remaining 3 marbles are selected from 4 of other colours

Thus $n_{1}=\binom{3}{2}\binom{4}{3}=\frac{3!}{2!}\cdot \frac{4!}{3!}=12$

2)We select all the 3 red marbles and the remaining 2 are selected from the remaining 4 marbles

$n_2=\binom{4}{2}=\frac{4!}{2!\cdot 2!}=6$

Thus the total number of ways are $n_1+n_2=12+6=18$