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If repetitions are not allowed, the number of numbers consisting of 4 digits and divisible by 5 and formed out of 0, 1, 2, 3, 4, 5, 6 is
- a)220
- b)240
- c)370
- d)588
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If repetitions are not allowed, the number of numbers consisting of 4 ...
Your approach is fine except for you are missing the repeated digit. Here is a lazy solution:
Imagine we only have 0,1,2,3,4,5,6, then your sums become:
0:6*5*4=120
5:5*5*4=100
Therefore there are at least 220
Most Upvoted Answer
If repetitions are not allowed, the number of numbers consisting of 4 ...
6P3 + 6P3 – 5P2 = 220
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Community Answer
If repetitions are not allowed, the number of numbers consisting of 4 ...
Approach:
To find the number of 4-digit numbers that are divisible by 5 and consist of the digits 0, 1, 2, 3, 4, 5, 6 without repetition, we need to follow a systematic approach.
Explanation:
1. Units digit:
Since the number has to be divisible by 5, the units digit can only be 0 or 5.
2. Thousands digit:
Since repetitions are not allowed, the thousands digit can be any of the remaining 5 digits (1, 2, 3, 4, 6).
3. Hundreds and tens digit:
The hundreds and tens digit can be any of the remaining 4 digits after the thousands and units digit have been chosen.
Calculation:
Number of choices for units digit = 2 (0 or 5)
Number of choices for thousands digit = 5 (1, 2, 3, 4, 6)
Number of choices for hundreds and tens digit = 4 (remaining 4 digits)
Total number of numbers = 2 * 5 * 4 = 40
Since we are looking for 4-digit numbers, the first digit cannot be 0. Therefore, the total number of such numbers = 40 - 1 = 39
Therefore, the correct answer is option 'A' (220).
To find the number of 4-digit numbers that are divisible by 5 and consist of the digits 0, 1, 2, 3, 4, 5, 6 without repetition, we need to follow a systematic approach.
Explanation:
1. Units digit:
Since the number has to be divisible by 5, the units digit can only be 0 or 5.
2. Thousands digit:
Since repetitions are not allowed, the thousands digit can be any of the remaining 5 digits (1, 2, 3, 4, 6).
3. Hundreds and tens digit:
The hundreds and tens digit can be any of the remaining 4 digits after the thousands and units digit have been chosen.
Calculation:
Number of choices for units digit = 2 (0 or 5)
Number of choices for thousands digit = 5 (1, 2, 3, 4, 6)
Number of choices for hundreds and tens digit = 4 (remaining 4 digits)
Total number of numbers = 2 * 5 * 4 = 40
Since we are looking for 4-digit numbers, the first digit cannot be 0. Therefore, the total number of such numbers = 40 - 1 = 39
Therefore, the correct answer is option 'A' (220).
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If repetitions are not allowed, the number of numbers consisting of 4 digits and divisible by 5 and formed out of 0, 1, 2, 3, 4, 5, 6 isa)220b)240c)370d)588Correct answer is option 'A'. Can you explain this answer?
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