Suppose there are 19 marbles in a bag: 5 red, 6 green, and 8 blue ones. How many ways can 5 marbles be selected if exactly 2 marbles are red and 3 are another color?
How do I remove repetitions from a combinatorics problem?
1
$\begingroup$
combinatorics
-
1I'm not really sure what the title of the post is asking. If you want to choose $5$ marbles, $2$ of which are red and $3$ of which are not red, then there are no repetitions here. You need the Multiplication principle here (http://mathworld.wolfram.com/MultiplicationPrinciple.html). – 2012-01-18
-
0Maybe, it's also good to ask, whether OP is aware of the [principle of inclusion-exclusion](http://en.wikipedia.org/wiki/Inclusion–exclusion_principle)? – 2012-01-18
1 Answers
3
This is a simple problem, and you don't need inclusion-exclusion, removing repetitions, and the like.
# of ways = (ways to select 2 red)*(ways to select any 3 of other colors)
= C(5,2)*C(14,3)
-
0I won't downvote, but for future reference I think that giving answers outright should be discouraged, especially when the OP has yet to respond to comments in the OP can discuss the problem. – 2012-01-18
-
0@JavaMan: Ok, i'm new to this forum. I'll bear it in mind. – 2012-01-18