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3-digit numbers are formed using the digits 1, 3, 7 without repetition of digits. A number is randomly selected. What is the probability that the number is divisible by 3?
- a)0
- b)1/3
- c)1/4
- d)1/8
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
3-digit numbers are formed using the digits 1, 3, 7 without repetition...
- Divisibility rule of 3 : A number is completely divisible by 3 if the sum of its digits is divisible by 3
- nPr = n!/(n - r)!
Calculation:
Total number of three-digit numbers = 3P2 = 3!/(3 - 2)! = 6
Total number of three-digit numbers are 137, 173, 371, 317, 713, 731
Total number of outcomes = 6
Since Sum of digits is 11 which is not a multiple of 3
So, The favorable outcome is 0
∴ The probability that the number is divisible by 3 is 0/6 = 0.
Total number of three-digit numbers = 3P2 = 3!/(3 - 2)! = 6
Total number of three-digit numbers are 137, 173, 371, 317, 713, 731
Total number of outcomes = 6
Since Sum of digits is 11 which is not a multiple of 3
So, The favorable outcome is 0
∴ The probability that the number is divisible by 3 is 0/6 = 0.
Most Upvoted Answer
3-digit numbers are formed using the digits 1, 3, 7 without repetition...
To find the probability that a 3-digit number formed using the digits 1, 3, and 7 is divisible by 3, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
Since we are forming 3-digit numbers without repetition, we have 3 choices for the hundreds place, 2 choices for the tens place, and 1 choice for the units place. Therefore, the total number of 3-digit numbers that can be formed is 3 * 2 * 1 = 6.
Favorable Outcomes:
To determine the favorable outcomes, we need to consider the divisibility rule for 3. A number is divisible by 3 if the sum of its digits is divisible by 3.
We can form 3-digit numbers using the digits 1, 3, and 7 in the following ways:
1. Numbers that are divisible by 3:
- 137 (1 + 3 + 7 = 11, not divisible by 3)
- 173 (1 + 7 + 3 = 11, not divisible by 3)
- 317 (3 + 1 + 7 = 11, not divisible by 3)
- 371 (3 + 7 + 1 = 11, not divisible by 3)
- 713 (7 + 1 + 3 = 11, not divisible by 3)
- 731 (7 + 3 + 1 = 11, not divisible by 3)
There are no numbers that are divisible by 3.
Therefore, the number of favorable outcomes is 0.
Probability:
The probability of an event is given by the number of favorable outcomes divided by the total number of outcomes.
In this case, the probability that the number is divisible by 3 is 0 divided by 6, which equals 0.
Therefore, the correct answer is option A) 0.
Total Number of Outcomes:
Since we are forming 3-digit numbers without repetition, we have 3 choices for the hundreds place, 2 choices for the tens place, and 1 choice for the units place. Therefore, the total number of 3-digit numbers that can be formed is 3 * 2 * 1 = 6.
Favorable Outcomes:
To determine the favorable outcomes, we need to consider the divisibility rule for 3. A number is divisible by 3 if the sum of its digits is divisible by 3.
We can form 3-digit numbers using the digits 1, 3, and 7 in the following ways:
1. Numbers that are divisible by 3:
- 137 (1 + 3 + 7 = 11, not divisible by 3)
- 173 (1 + 7 + 3 = 11, not divisible by 3)
- 317 (3 + 1 + 7 = 11, not divisible by 3)
- 371 (3 + 7 + 1 = 11, not divisible by 3)
- 713 (7 + 1 + 3 = 11, not divisible by 3)
- 731 (7 + 3 + 1 = 11, not divisible by 3)
There are no numbers that are divisible by 3.
Therefore, the number of favorable outcomes is 0.
Probability:
The probability of an event is given by the number of favorable outcomes divided by the total number of outcomes.
In this case, the probability that the number is divisible by 3 is 0 divided by 6, which equals 0.
Therefore, the correct answer is option A) 0.
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Community Answer
3-digit numbers are formed using the digits 1, 3, 7 without repetition...
- Divisibility rule of 3 : A number is completely divisible by 3 if the sum of its digits is divisible by 3
- nPr = n!/(n - r)!
Calculation:
Total number of three-digit numbers = 3P2 = 3!/(3 - 2)! = 6
Total number of three-digit numbers are 137, 173, 371, 317, 713, 731
Total number of outcomes = 6
Since Sum of digits is 11 which is not a multiple of 3
So, The favorable outcome is 0
∴ The probability that the number is divisible by 3 is 0/6 = 0.
Total number of three-digit numbers = 3P2 = 3!/(3 - 2)! = 6
Total number of three-digit numbers are 137, 173, 371, 317, 713, 731
Total number of outcomes = 6
Since Sum of digits is 11 which is not a multiple of 3
So, The favorable outcome is 0
∴ The probability that the number is divisible by 3 is 0/6 = 0.
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