Terry Lee combinations question (1 Viewer)

[porcupinetree]

Could somebody please point out the flaw in my method for this question from Terry Lee? If it's hard to understand from the picture, my idea was to choose 1 ball from each colour set (hence [11C1]^4), and choose 2 more from any of the remaining 40.

 

[InteGrand]

Could somebody please point out the flaw in my method for this question from Terry Lee? If it's hard to understand from the picture, my idea was to choose 1 ball from each colour set (hence [11C1]^4), and choose 2 more from any of the remaining 40.

Your way over-counts, because when you say you choose 1 ball from each set, then choose 2 more randomly, the 2 you choose randomly may be ones that in another case you counted as choosing as "1" from a set.

E.g. Say ball X is the orange ball #2. In your method, you count the following as different, when they should be considered the same:

• Pick X as the "1" to be orange, then pick 2 randomly after picking "1" for each other colour, and say one of these two picked is Ball Y, which is a different orange ball (say #6).

• Pick ball Y as the "1" to be orange, and pick X as one of the 2 randomly picked, with the other balls picked the same as the previous dot point.

 

[porcupinetree]

Your way over-counts, because when you say you choose 1 ball from each set, then choose 2 more randomly, the 2 you choose randomly may be ones that in another case you counted as choosing as "1" from a set.

E.g. Say ball X is the orange ball #2. In your method, you count the following as different, when they should be considered the same:

• Pick X as the "1" to be orange, then pick 2 randomly after picking "1" for each other colour, and say one of these two picked is Ball Y, which is a different orange ball (say #6).

• Pick ball Y as the "1" to be orange, and pick X as one of the 2 randomly picked, with the other balls picked the same as the previous dot point.

Ah, thankyou so much, I see now. One final question: what is the reason for the 2C1 in Terry's solution? I understand all of his other working but I don't see what the 2C1 is there for

 

[InteGrand]

Ah, thankyou so much, I see now. One final question: what is the reason for the 2C1 in Terry's solution? I understand all of his other working but I don't see what the 2C1 is there for

 

[porcupinetree]

Yeah that's what I was thinking. Cheers for your help