A bag contains $4$ red and $6$ white marbles. How many ways can $5$ marbles be selected if exactly $2$ must be red?

Question

A bag contains $4$ red and $6$ white marbles. How many ways can $5$ marbles be selected if exactly $2$ must be red?

Is it $120$?

Yes, you´re right. ${4\choose 2} \cdot {6 \choose 5-2}=6\cdot 20=120$ — callculus42, Jun 05 '16 at 06:14
Yes, it is. But try to include your reasoning in your posts so that others can point out your mathematically or logical mistake in case it is wrong. Also, if possible try to make your titles more specific; there are dozens of questions using marbles asked on the site. — Em., Jun 05 '16 at 06:45

score 3 · Answer 1 · answered Jun 05 '16 at 06:17

3

We choose $2$ marbles from the $4$ red ones. For each of these $\binom{4}{2}$ choices, there are $\binom{6}{3}$ ways to choose the three white marbles. So you are correct:

$$\binom{4}{2}\binom{6}{3}=6 \cdot 20 = \boxed{120}$$

answered Jun 05 '16 at 06:17

Zubin Mukerjee

17,832

1

Hmm you were right, order doesn't matter in this case. – Chee Han Jun 05 '16 at 06:20

A bag contains $4$ red and $6$ white marbles. How many ways can $5$ marbles be selected if exactly $2$ must be red?

1 Answers1