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Three integers are at random chosen between 0 and 9 inclusive. What is

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gonebada93
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Three integers are at random chosen between 0 and 9 inclusive. What is [#permalink] New post   08 May 2016, 15:34
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Three integers are at random chosen between 0 and 9 inclusive. What is the probability that each number is different ?

A. 18/25
B. 4/5
C. 81/100
D. 9/10
E. 1
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A
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Re: Three integers are at random chosen between 0 and 9 inclusive. What is [#permalink] New post   09 May 2016, 04:01
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Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8

Probability = 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25

Answer: A
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Re: Three integers are at random chosen between 0 and 9 inclusive. What is [#permalink] New post   10 May 2016, 08:16
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(Prob. of choosing any one from 10) * (Prob. of not choosing the first one) * (Prob. of not choosing the first two)
\(1 * (1-\frac{1}{10}) * (1-\frac{2}{10})\)
=>\(1 * \frac{9}{10} * \frac{8}{10}\)
=>\(\frac{72}{100}\)
=>\(\frac{18}{25}\)

Option A
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Three integers are at random chosen between 0 and 9 inclusive. What is [#permalink] New post   20 May 2018, 15:53
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First selection can be any 10 numbers, inclusive: 10/10 = 1
2nd selection will be reduced by 1 (because it has to be different from the 1st selection) : 9/10
3rd selection will be reduced by 2 (because it has to be different from selection 1 and selection 2): 8/10

1* (9/10) * (8/10) = 72/100
reduces down to 18/25

Answer A
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Re: Three integers are at random chosen between 0 and 9 inclusive. What is [#permalink] New post   20 May 2018, 19:37
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Step 1: Probability of selecting 3 integers without constraint - 10*10*10
Total number of possible outcomes = 1000

Step 2:
The probability of selecting first integer = 10
The probability of selecting second integer = 9 (Excluding the first digit)
The probability of selecting third integer = 8 (Excluding first and second digits)

Number of ways of selecting 3 different integers = 10*9*8 = 720

Total probability = 720/1000 = 72/100 = 18/25

Ans: A
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Re: Three integers are at random chosen between 0 and 9 inclusive. What is [#permalink] New post   24 May 2018, 13:27
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gonebada93 wrote:
Three integers are at random chosen between 0 and 9 inclusive. What is the probability that each number is different ?

A. 18/25
B. 4/5
C. 81/100
D. 9/10
E. 1


Let’s choose the first integer. . The probability that the second integer is different (from the first) is 9/10. The probability that the third integer is different (from the first and second) is 8/10.

Therefore, the probability that each number is different is 9/10 x 8/10 = 72/100 = 18/25.

Answer: A
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Re: Three integers are at random chosen between 0 and 9 inclusive. What is [#permalink] New post   01 Nov 2019, 20:04
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gonebada93 wrote:
Three integers are at random chosen between 0 and 9 inclusive. What is the probability that each number is different ?

A. 18/25
B. 4/5
C. 81/100
D. 9/10
E. 1



The probability that the first number is different is 10/10 = 1 (since no other numbers have been chosen yet). The probability that the second number is different from the first is 9/10, and the probability the third number is different from the first two is 8/10 = 4/5. Therefore, the probability that all three numbers are different is 1 x 9/10 x 4/5 = 36/50 = 18/25.

Answer: A
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Re: Three integers are at random chosen between 0 and 9 inclusive. What is [#permalink] New post   06 Oct 2022, 07:42
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Re: Three integers are at random chosen between 0 and 9 inclusive. What is [#permalink]
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