Permutions and Combinations

I

izzy43

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So I'm being asked: A box contains 10 red marbles, 9 green marbles, and 7 black marbles. A sample of 11 marbles is to be picked from the box:


  1. [FONT=verdana, helvetica, sans-serif]How many samples contain at least 1 red marble?[/FONT]
[FONT=verdana, helvetica, sans-serif]​[/FONT]I know that to do this problem I would find all the combinations possible and subtract the number of combinations that have no red marbles from it.
C(26,11) - C(10,0) * C(16,11) = at least 1 red.


  1. How many samples contain exactly 5 green marbles or exactly 3 black marbles?
[FONT=verdana, helvetica, sans-serif]​I know that to do this problem I have to take the OR into account. So I'd do two separate combination things (A)= exactly 5 green marbles , (B)= Exactly 3 green marbles and (C) The union of both A and B, and placing in the missing marble combination to complete the sample.
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(A)= C(10,5)*C(16,6)
(B)= C(7,3)*C(19,8)
(C)= C(10,5)*C(7,3)*(9,4)

I add A and B and subtract C and get my answer.


  1. How many samples contain exactly 7 red marbles or exactly 6 green marbles?
​I would think that to solve this problem i'd have to approach it the same way as I did with the one before but the sample is of 11, and choosing both at the same time brings me to a higher sample number. Could someone help me out with this portion? THANKS!

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izzy43 said:
So I'm being asked: A box contains 10 red marbles, 9 green marbles, and 7 black marbles. A sample of 11 marbles is to be picked from the box:

  1. How many samples contain exactly 5 green marbles or exactly 3 black marbles?
​I know that to do this problem I have to take the OR into account. So I'd do two separate combination things (A)= exactly 5 green marbles , (B)= Exactly 3 green marbles and (C) The union of both A and B, and placing in the missing marble combination to complete the sample.
Click to expand...

\(\displaystyle \#(A\cup B)=\#(A)+\#(B)-\#(A\cap B)=(_9C_5\cdot _{17}C_6)+_(7C_3\cdot _{7}C_6)-( _9C_5\cdot _{7}C_3\cdot _{10}C_3)\)
 
izzy43 said:
So I'm being asked: A box contains 10 red marbles, 9 green marbles, and 7 black marbles. A sample of 11 marbles is to be picked from the box:

How many samples contain exactly 5 green marbles or exactly 3 black marbles?
​I know that to do this problem I have to take the OR into account. So I'd do two separate combination things (A)= exactly 5 green marbles , (B)= Exactly 3 green marbles and (C) The union of both A and B, and placing in the missing marble combination to complete the sample.

(A)= C(10,5)*C(16,6)
(B)= C(7,3)*C(19,8)
(C)= C(10,5)*C(7,3)*(9,4)

I add A and B and subtract C and get my answer.


  1. How many samples contain exactly 7 red marbles or exactly 6 green marbles?
​I would think that to solve this problem i'd have to approach it the same way as I did with the one before but the sample is of 11, and choosing both at the same time brings me to a higher sample number. Could someone help me out with this portion? THANKS!
Click to expand...

You can't have 7 red and 6 green, so your C = 0. Other than that it is the same.
 
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