There are 7 red and 5 yellow fish in an aquarium. Three fish are randomly...

doturitip9

doturitip9

Answered

2022-07-14

There are 7 red and 5 yellow fish in an aquarium. Three fish are randomly caught in a net. Find the probability that the fish were:
a) All red
b) Not all of the same color.

I have solved this question using the method for dependent events as follows:
a) 7 12 6 11 5 10 = 210 1320
b) 1 ( 7 12 6 11 5 10 + 5 12 4 11 3 10 ) = 1170 1320
Is it possible to use combinations to solve this question? If yes, how?

Answer & Explanation

kawiarkahh

kawiarkahh

Expert

2022-07-15Added 15 answers

(a)
( 7 3 ) ( 12 3 )
You can show that this equals what you did.
( 7 3 ) ( 12 3 ) = 7 ! 3 ! 4 ! 12 ! 3 ! 9 ! = 7 6 5 3 2 1 3 2 1 12 11 10 = 7 12 6 11 5 10
(b)
1 ( 7 3 ) ( 12 3 ) ( 5 3 ) ( 12 3 )
Wronsonia8g

Wronsonia8g

Expert

2022-07-16Added 1 answers

a)
( 7 3 ) ( 5 0 ) ( 12 3 )
b)
1 ( 7 3 ) ( 5 0 ) ( 12 3 ) ( 7 0 ) ( 5 3 ) ( 12 3 )

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