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23 Sep 2025, 23:29
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
59% (03:15) correct
41%
(02:36)
wrong
based on 102
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A five-digit number is formed with the help of digits from 0 to 6; without repetition, find the probability that the number formed is divisible by 5.
A. 1/3
B. 5/180
C. 5/18
D. 11/36
E. 71/ 147
Screenshot 2025-09-24 11.55.42 AM.png [ 45.2 KiB | Viewed 941 times ]
A. 1/3
B. 5/180
C. 5/18
D. 11/36
E. 71/ 147
Attachment:
Screenshot 2025-09-24 11.55.42 AM.png [ 45.2 KiB | Viewed 941 times ]
23 Sep 2025, 23:58
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To find the probability, we must determine the total number of possible five-digit numbers and the number of five-digit numbers divisible by 5. The probability is the ratio of these two values.
Step 1: Total Possible Outcomes
A five-digit number cannot start with the digit 0. The digits available are {0,1,2,3,4,5,6}, a total of 7 digits. We must form a five-digit number without repetition.
• For the first digit (ten thousands place), there are 6 choices (1, 2, 3, 4, 5, 6).
• For the second digit, there are 6 choices (any of the remaining 6 digits, including 0).
• For the third digit, there are 5 choices.
• For the fourth digit, there are 4 choices.
• For the fifth digit, there are 3 choices.
Total possible numbers = 6×6×5×4×3=2160
Step 2: Favorable Outcomes
A number is divisible by 5 if and only if its last digit is either 0 or 5. We must consider two separate cases.
Case 1: The last digit is 0.
• The last digit has 1 choice (0).
• The first digit can be any of the remaining 6 digits.
• The second digit has 5 choices.
• The third digit has 4 choices.
• The fourth digit has 3 choices.
Number of possibilities = 6×5×4×3×1=360
Case 2: The last digit is 5.
• The last digit has 1 choice (5).
• The first digit cannot be 0 or 5. So, there are 5 choices (1, 2, 3, 4, 6).
• The second digit has 5 choices (including 0 now).
• The third digit has 4 choices.
• The fourth digit has 3 choices.
Number of possibilities = 5×5×4×3×1=300
Total favorable numbers = 360+300=660
Step 3: Find the Probability
Required probability = # of Favorable Outcomes / Total Possible Outcomes = 660 / 2160 = 11/36
Hence choice (D) is right.
Step 1: Total Possible Outcomes
A five-digit number cannot start with the digit 0. The digits available are {0,1,2,3,4,5,6}, a total of 7 digits. We must form a five-digit number without repetition.
• For the first digit (ten thousands place), there are 6 choices (1, 2, 3, 4, 5, 6).
• For the second digit, there are 6 choices (any of the remaining 6 digits, including 0).
• For the third digit, there are 5 choices.
• For the fourth digit, there are 4 choices.
• For the fifth digit, there are 3 choices.
Total possible numbers = 6×6×5×4×3=2160
Step 2: Favorable Outcomes
A number is divisible by 5 if and only if its last digit is either 0 or 5. We must consider two separate cases.
Case 1: The last digit is 0.
• The last digit has 1 choice (0).
• The first digit can be any of the remaining 6 digits.
• The second digit has 5 choices.
• The third digit has 4 choices.
• The fourth digit has 3 choices.
Number of possibilities = 6×5×4×3×1=360
Case 2: The last digit is 5.
• The last digit has 1 choice (5).
• The first digit cannot be 0 or 5. So, there are 5 choices (1, 2, 3, 4, 6).
• The second digit has 5 choices (including 0 now).
• The third digit has 4 choices.
• The fourth digit has 3 choices.
Number of possibilities = 5×5×4×3×1=300
Total favorable numbers = 360+300=660
Step 3: Find the Probability
Required probability = # of Favorable Outcomes / Total Possible Outcomes = 660 / 2160 = 11/36
Hence choice (D) is right.
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27 Sep 2025, 04:43
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To form a 5-digit number divisible by 5, we need to ensure that the number ends in either 0 or 5.
Case 1: The last digit is 0
Using slot method: 6x5x4x3x1
Case 2: The last digit is 5
Using slot method: 5x5x4x3x1 (as the number cannot start with 0 otherwise it won't be a 5-digit)
Total outcome : As mentioned above, the number cannot start with 0, so, 6x6x5x4x3
To find: P(5-digit no divisible by 5) = No. ends with 0 or no. ends with 5/Total outcome (6x5x4x3 + 5x5x4x3)/6x6x5x4x3 = 11/36
Case 1: The last digit is 0
Using slot method: 6x5x4x3x1
Case 2: The last digit is 5
Using slot method: 5x5x4x3x1 (as the number cannot start with 0 otherwise it won't be a 5-digit)
Total outcome : As mentioned above, the number cannot start with 0, so, 6x6x5x4x3
To find: P(5-digit no divisible by 5) = No. ends with 0 or no. ends with 5/Total outcome (6x5x4x3 + 5x5x4x3)/6x6x5x4x3 = 11/36
