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Arlecino [84]
2 years ago
6

How many integers between 100 and 999 (inclusive) have distinct digits

Mathematics
1 answer:
daser333 [38]2 years ago
5 0

Answer:

648

Step-by-step explanation:

Running this in Python, with the code as follows,

import math

cur_numbers = [0] * 3

num = 0

for i in range(100, 1000):

   cur_numbers[2] = i % 10

   i = math.floor(i/10)

   cur_numbers[1] = i % 10

   i = math.floor(i/10)

   cur_numbers[0] = i % 10

   if(len(set(cur_numbers)) == 3):

       num += 1

       print(cur_numbers)

       

print(num), we get 648 as our answer.

Another way to solve this is as follows:

There are 9 possibilities for the hundreds digit (1-9). Then, there are 10 possibilities for the tens digit, but we subtract 1 because it can't be the 1 same digit as the hundreds digit. For the ones digit, there are 10 possibilities, but we subtract 1 because it can't be the same as the hundreds digit and another 1 because it can't be the same as the tens digit. Multiplying these out, we have

9 possibilities for the hundreds digit x 9 possibilities for the tens digit x 8 possibilities for the ones digit  = 648

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Aneli [31]

Answer:

Step-by-step explanation:

1) 2x -y = 1 -------1

3x - y = -6 ------2

Subtract eqn 2 from eqn 1

-x = 1--6 = 7

x = -7

Put x= -7 in eqn 1

2*-7-y = 1

-14-y = 1

- y = 15

y = -15

2) 4x +2y = 10------1

y = 4x + 2--------2

Put eqn 2 in eqn 1

4x + 2 ( 4x+ 2) = 10

4x + 8x + 4 = 10

12x = 6

x = 6/12 = 1/2

Put x = 1/2 in eqn 2

y = 4* 1/2 + 2= 2 + 2

= 4

3) 6x - y = 2------1

y = 3x + 4---------2

Put eqn 2 in eqn 1

6x - (3x +4) = 2

6x - 3x - 4 = 2

3x = 6

x = 2

y = 3*2 + 4 = 6 + 4

= 10

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3 years ago
A biology experiment calls for 10 milliliters of water. How much water does the experiment call for in centiliters? (a.1 (b10 (c
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3 years ago
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1. parallelogram

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4. parallelogram

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3 years ago
The computer that controls a bank's automatic teller machine crashes a mean of 0.6 times per day. What is the probability that,
professor190 [17]

Answer:

0.2103 = 21.03% probability that, in any seven-day week, the computer will crash less than 3 times.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

Mean of 0.6 times a day

7 day week, so \mu = 7*0.6 = 4.2

What is the probability that, in any seven-day week, the computer will crash less than 3 times? Round your answer to four decimal places.

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

In which

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-4.2}*(4.2)^{0}}{(0)!} = 0.0150

P(X = 1) = \frac{e^{-4.2}*(4.2)^{1}}{(1)!} = 0.0630

P(X = 2) = \frac{e^{-4.2}*(4.2)^{2}}{(2)!} = 0.1323

So

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0150 + 0.0630 + 0.1323 = 0.2103

0.2103 = 21.03% probability that, in any seven-day week, the computer will crash less than 3 times.

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3 years ago
(x-y) (x-1,y+3) (I need the answer pls)
SVEN [57.7K]

Answer:

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Step-by-step explanation:

1: Multiply the second parentheses by each term from the first parentheses

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2: Distribute x through parentheses

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3 years ago
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