To use that in a computation, you need to simplify it. Where is that simplification?Choosing 3 out of 5 balls--> 5c3
To use that in a computation, you need to simplify it. Where is that simplification?Choosing 1 out of 2 balls --> 2c1
To use that in a computation, you need to simplify it. Where is that simplification?Choosing 1 out of 1 --> 1c1
Of course I know how to do them. My point is that you have not simplified them because you have not shown any computations with them so we have no clue what you are going to do with them.
Yes at last a computation with reasoning associated with it. The reasoning is not easy to follow but is quite sound. The computation is correct.Now for a particular combination (b1 b2 b3 , b4, b5)
Main point: For a event suppose, Triplets have three options of sitting in any one box so it chooses one , then there are two boxes left for 2 Single Distinct balls ; so ball 4 have 2 options so suppose b4 sits in any ONE out of 2 box and the remaining one box can be taken by b5 . So , 6 ways ?
You have not said what the indicated computation represents. That makes it impossible to understand. Moreover, because you have not told us what you are trying to calculate, how do we know if you made a mistake or not? Finally in no previous step have you given 3!. Where did that come from? And what does that expression simplify to?So, 5c3 * 2c1 * 1c1 * 3! . What is so hard to understand?
What is the mistake that am i not able to catch?[
You said your answer was 300. Now, according to my reckoning the expression above simplifies to
[MATH]\dbinom{5}{3} * \dbinom{2}{1} * \dbinom{1}{1} * 3! = 10 * 2 * 1 * 6 = 120 \ne 300.[/MATH]
So I have no idea how you got an answer of 300.
EDIT: By the way, 60 is a relevant number so the 120 does look as though you double counted something, but I do not know why you double counted because you did not tell us why you stuck those numbers together the way you did.
EDIT2: And I agree that combinatorics is hard. The first time I solved this problem I did it wrong. Only trying a different method showed me my error.
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