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Let us assume we have an eight face die numbered from 1 to 8. What is the probability that exactly two of the eight numbers appear on the top face in the five throws of an unbiased die?
  • a)
    840/32768
  • b)
    896/32768
  • c)
    700/32768
  • d)
    644/32768
Correct answer is option 'A'. Can you explain this answer?
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Let us assume we have an eight face die numbered from 1 to 8. What is...
Probability of exactly two numbers appearing on the top face in five throws of an eight-faced die

To find the probability of exactly two numbers appearing on the top face in five throws of an eight-faced die, we need to calculate the total number of favorable outcomes and divide it by the total number of possible outcomes.

Total number of possible outcomes:
Since each throw of the die can result in any number from 1 to 8, there are 8 possible outcomes for each throw. As there are a total of 5 throws, the total number of possible outcomes is 8^5 = 32768.

Total number of favorable outcomes:
To calculate the total number of favorable outcomes, we need to consider the different ways in which exactly two numbers can appear on the top face in five throws.

Case 1: Two different numbers appear twice each, and one number appears once.
In this case, we need to choose two numbers out of 8, which can be done in 8C2 ways. Once the two numbers are chosen, we need to arrange them in the five throws, which can be done in 5C2 ways. The remaining number can be chosen in 6 ways. Therefore, the total number of favorable outcomes for this case is 8C2 * 5C2 * 6 = 28 * 10 * 6 = 1680.

Case 2: One number appears three times, and two different numbers appear once each.
In this case, we need to choose one number out of 8, which can be done in 8C1 ways. Once the number is chosen, we need to arrange it in the five throws, which can be done in 5C3 ways. The remaining two numbers can be chosen in 7C2 ways. Therefore, the total number of favorable outcomes for this case is 8C1 * 5C3 * 7C2 = 8 * 10 * 21 = 1680.

Total number of favorable outcomes:
The total number of favorable outcomes is the sum of the favorable outcomes from both cases: 1680 + 1680 = 3360.

Probability:
Finally, we can calculate the probability by dividing the total number of favorable outcomes by the total number of possible outcomes.
Probability = Total number of favorable outcomes / Total number of possible outcomes = 3360 / 32768 = 840 / 8192 = 840 / 32768.

Hence, the correct answer is option A) 840/32768.
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Community Answer
Let us assume we have an eight face die numbered from 1 to 8. What is...
Total Number of possible outcomes = 85
Selecting any two numbers from 1 to 8 = 8C2
These two numbers should appear in all 5 throws. Let us say, x and y are those two numbers. Thus, first throw should result in either x or y. Similarly for all subsequent throws.
But, all throws should not result in the same number.
Required probability=8C2*(25 - 2)/ 85
= 840/32768.
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Group QuestionAnswer the following questions based on the information given below.A certain building built up in the rectangular shape contains 10 apartments numbered from 0 to 9. The area of each apartment is dependent on the floor on which it is situated. Further all the apartments on any floors are of same size. However the total area of all the apartments put together on each of the floor is equal. The top floor is considered as row 1 in this building.The apartments are however are not numbered in serial fashion. The clues below indicate the apartment numbers situated on any of the floors.1. The sum of four apartment numbers in 4th row is 28.2. The biggest apartment number in row 3 is in the central apartment of the floor.3. The 3rd apartment number from the left in the bottom row isnt 7.4. The sum of rightmost apartment numbers in the four rows put together is 11.5. The apartments numbered 0 and 5 are in different rows of this building.6. The number of the apartment at the top minus the number of leftmost apartment in row 2 is 4. 7. The sum of leftmost apartment numbers in the four rows sum to 20.Q.Which apartment number has the largest area? Correct answer is '6'. Can you explain this answer?

A certain building built up in the rectangular shape contains 10 apartments numbered from 0 to 9. The area of each apartment is dependent on the floor on which it is situated. Further all the apartments on any floors are of same size. However the total area of all the apartments put together on each of the floor is equal. The top floor is considered as row 1 in this building.The apartments are however are not numbered in serial fashion. The clues below indicate the apartment numbers situated on any of the floors.1. The sum of four apartment numbers in 4th row is 28.2. The biggest apartment number in row 3 is in the central apartment of the floor.3. The 3rd apartment number from the left in the bottom row isnt 7.4. The sum of rightmost apartment numbers in the four rows put together is 11.5. The apartments numbered 0 and 5 are in different rows of this building.6. The number of the apartment at the top minus the number of leftmost apartment in row 2 is 4. 7. The sum of leftmost apartment numbers in the four rows sum to 20.Q.Which row has the least sum of all the apartments? Correct answer is '2'. Can you explain this answer?

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Let us assume we have an eight face die numbered from 1 to 8. What is the probability that exactly two of the eight numbers appear on the top face in the five throws of an unbiased die?a)840/32768b)896/32768c)700/32768d)644/32768Correct answer is option 'A'. Can you explain this answer?
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