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In a poker set there are 90 chips numbered from 1 to 90. Dan picks 3 chips at random, one after the other, without replacement. What is the probability that the numbers on the chips, in the order that he picks them are in descending order?
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In a poker set there are 90 chips numbered from 1 to 90. Dan picks 3 c...
Probability of Picking Chips in Descending Order
To find the probability of picking chips in descending order, we need to first determine the total number of possible outcomes. Then, we need to determine the number of outcomes that satisfy the given condition.
Step 1: Total Number of Possible Outcomes
The number of ways to pick three chips from a set of 90 chips is:
C(90,3) = (90!)/(3!(90-3)!) = 117,480
Step 2: Number of Outcomes in Descending Order
To pick chips in descending order, the largest number must be picked first, followed by the second-largest number, and then the third-largest number.
The number of ways to pick the largest chip is 90.
After the largest chip has been picked, there are 89 chips remaining. The number of ways to pick the second-largest chip is 89.
After the two largest chips have been picked, there are 88 chips remaining. The number of ways to pick the third-largest chip is 88.
The total number of outcomes in descending order is:
(90)(89)(88) = 704,880
Step 3: Probability of Picking Chips in Descending Order
The probability of picking chips in descending order is:
Probability = (Number of Outcomes in Descending Order) / (Total Number of Possible Outcomes)
Probability = 704,880 / 117,480 = 0.006
Conclusion
The probability of picking chips in descending order is 0.006 or 0.6%.
This means that if Dan picks three chips at random, the chance of him picking chips in descending order is very low.
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In a poker set there are 90 chips numbered from 1 to 90. Dan picks 3 chips at random, one after the other, without replacement. What is the probability that the numbers on the chips, in the order that he picks them are in descending order??
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