1. ## combinations choosing

In a bag are ten red marbles, ten black marbles, ten yellow marbles, and ten green marbles all numbered from 1 to 10. A person is going to reach into the bag and draw out five marbles.

a. How many possible outcomes are there?
im pretty sure this is 40C5
b. How many outcomes contain no red marbles?
c. How many of these outcomes contain at least one red marble?
d. How many of these outcomes contain no marble numbered 5?
e. How many of these outcomes contain at least one marble numbered with a 5?

2. Originally Posted by ihavvaquestion
In a bag are ten red marbles, ten black marbles, ten yellow marbles, and ten green marbles all numbered from 1 to 10. A person is going to reach into the bag and draw out five marbles.

a. How many possible outcomes are there?
im pretty sure this is 40C5
b. How many outcomes contain no red marbles?
c. How many of these outcomes contain at least one red marble?
d. How many of these outcomes contain no marble numbered 5?
e. How many of these outcomes contain at least one marble numbered with a 5?
Dear ihavvaquestion,

For (a) you should consider the fact that there are similar marbles of the same colour. If all the marbles are distinct from each other your answer is correct.

3. since the marbles are all numbered, then 40C5 should be correct then right?

b) how many outcomes contain no red marbles?

would this just be 30C5 taking the red marbles out?

c) how many have at least one red marble?

would this be 40C5 - 30C5?

d) how many have no marble numbered 5?
40C5 - 36C5 ???
e) how many have at least one marble numbered 5?
40C5 - 4C5 ?????

i am new to this stuff...i dont know if im on the right track or not! can someone please help me out

4. Originally Posted by ihavvaquestion
since the marbles are all numbered, then 40C5 should be correct then right?

b) how many outcomes contain no red marbles?

would this just be 30C5 taking the red marbles out?

c) how many have at least one red marble?

would this be 40C5 - 30C5?

d) how many have no marble numbered 5?
40C5 - 36C5 ???
e) how many have at least one marble numbered 5?
40C5 - 4C5 ?????

i am new to this stuff...i dont know if im on the right track or not! can someone please help me out
If all the marbles are distinct then the answers for (a),(b) and (c) are correct.

However for (d);

There are a total of 36 marbles without the marbles numbered 5. Hence if we neglect the marbles numbered 5 there would be $\displaystyle ^{36}\textrm{C}_{5}$ arrangements.

Therefore the the arrangements that consist of at least one marble numbered '5' = $\displaystyle ^{40}\textrm{C}_{5}-^{36}\textrm{C}_{5}$

5. okay, so for no marbles numbered 5, we would just take out those marbles, and there would be 36C5 outcomes that contained no marbles numbered 5?

then for the outcomes that had at least one marble numbered five i would take the total outcomes 40C5 and subtract the total outcomes that contained no marbles numbered 5, 36C5???
40C5-36C5 marbles with at least 1 marble numbered 5

6. Originally Posted by ihavvaquestion
okay, so for no marbles numbered 5, we would just take out those marbles, and there would be 36C5 outcomes that contained no marbles numbered 5?

then for the outcomes that had at least one marble numbered five i would take the total outcomes 40C5 and subtract the total outcomes that contained no marbles numbered 5, 36C5???
40C5-36C5 marbles with at least 1 marble numbered 5
Dear ihavvaquestion,

Yes you are correct.