We have 3 that qualify as best three, say BBB, and 2 as bad say OO. Thus, the total outcomes can be

Iyana Macdonald

Iyana Macdonald

Answered question

2022-05-12

We have 3 that qualify as best three, say BBB, and 2 as bad say OO.
Thus, the total outcomes can be calculated as follows: 0 bad : This will be 1 as only one way to choose the best three 1 bad : This will be 3 ways. 'OBB' is one example and can be arranged in 3 ways. 2 bad : 3 ways.
Thus, the total outcomes according to me should be 7, not 10. What am I doing wrong?

Answer & Explanation

Eliezer Olson

Eliezer Olson

Beginner2022-05-13Added 16 answers

The flaw in your reasoning is in "1 bad : This will be 3 ways"
Correct # of ways for 1 bad, 2 good = ( 2 1 ) ( 3 2 )
The full expression, case wise, without any shortcuts, would be ( 2 0 ) ( 3 3 ) + ( 2 1 ) ( 3 2 ) + ( 2 2 ) ( 3 1 ) = 10
But why add up different cases ?
You directly get it as choosing any 3 out of the total of 5, viz. ( 5 3 )

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