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07 Aug 2003, 02:44
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There are six balls in a box. Three balls are marked with 1, three with 0. Three balls are taken at random without repetitions. In how many combinations will the product of the digits on the balls equal to 0?
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07 Aug 2003, 03:40
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The product of three numbers will equal ‘0’ if at least one of the numbers is zero. Another way is to substract a number of combinations when none of the numbers equal zero from a total number of combinations.
A total number of combinations of 3 balls out of 6 is 6C3=20. The number of combinations of all ones is 3C3=1. Thus, the number of combinations of none zero out of three is 20-1=19.
Double check the longer way (at least)
Number of combinations of exactly one zero (two '1'): 3C1*3C2=9
Number of combinations of exactly two zeros (one '1'): 3C2*3C1=9
Number of combinations of exactly tree zeros: 3C3=1
Add them all up and the answer is 19.
- Stolyar?
A total number of combinations of 3 balls out of 6 is 6C3=20. The number of combinations of all ones is 3C3=1. Thus, the number of combinations of none zero out of three is 20-1=19.
Double check the longer way (at least)
Number of combinations of exactly one zero (two '1'): 3C1*3C2=9
Number of combinations of exactly two zeros (one '1'): 3C2*3C1=9
Number of combinations of exactly tree zeros: 3C3=1
Add them all up and the answer is 19.
- Stolyar?
07 Aug 2003, 11:42
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Guys,
We are paying so much attention to combinations here. It is great, but I must say that another topic - promultation is a kind of deep forest for me.
If someone has any questions on promultation that he would like to post here, I would be grateful.
We are paying so much attention to combinations here. It is great, but I must say that another topic - promultation is a kind of deep forest for me.
If someone has any questions on promultation that he would like to post here, I would be grateful.
