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How many 5 digit telephone numbers can be constructed using the digits 0 to 9, if each number starts with 67 and no digit appears more than once?
- a)335
- b)336
- c)338
- d)337
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
How many 5digit telephone numbers can be constructed using the digits ...
Approach:
To construct a 5-digit telephone number starting with 67 without repeating any digit, we need to choose the remaining 3 digits from the set {0, 1, 2, 3, 4, 5, 8, 9}.
Calculation:
- Number of ways to choose the first digit (6): 1 way
- Number of ways to choose the second digit (7): 1 way
- Number of ways to choose the remaining 3 digits: 8P3 (permutations of 3 digits taken from 8) = 8*7*6 = 336 ways
- Total number of 5-digit telephone numbers: 1 * 1 * 336 = 336
Therefore, the correct answer is option (b) 336.
To construct a 5-digit telephone number starting with 67 without repeating any digit, we need to choose the remaining 3 digits from the set {0, 1, 2, 3, 4, 5, 8, 9}.
Calculation:
- Number of ways to choose the first digit (6): 1 way
- Number of ways to choose the second digit (7): 1 way
- Number of ways to choose the remaining 3 digits: 8P3 (permutations of 3 digits taken from 8) = 8*7*6 = 336 ways
- Total number of 5-digit telephone numbers: 1 * 1 * 336 = 336
Therefore, the correct answer is option (b) 336.
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Community Answer
How many 5digit telephone numbers can be constructed using the digits ...
Since, telephone number start with 67, so two digits is already fixed
Now, we have to arrangement of three digits from remaining eight digits (i.e., 0,1,2,3,4,5,8,9)
= 8 × 7 × 6
= 336 ways
Now, we have to arrangement of three digits from remaining eight digits (i.e., 0,1,2,3,4,5,8,9)
= 8 × 7 × 6
= 336 ways
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How many 5digit telephone numbers can be constructed using the digits 0 to 9,if each number starts with 67and no digit appears more than once?a)335b)336c)338d)337Correct answer is option 'B'. Can you explain this answer?
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