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The number of 5-digit numbers that can be made using the digits 1 and 2 and in which at least one digit is different, is
- a)30
- b)31
- c)32
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The number of 5-digit numbers that can be made using the digits 1 and ...
Total number of numbers without restriction 25.
Two numbers have all the digits equal. So, the required number of numbers = 25 - 2
Two numbers have all the digits equal. So, the required number of numbers = 25 - 2
Most Upvoted Answer
The number of 5-digit numbers that can be made using the digits 1 and ...
Number of 5-digit numbers that can be made using the digits 1 and 2 is a permutation problem. We need to count the number of arrangements of the digits 1 and 2 in a 5-digit number.
1. Counting the total number of 5-digit numbers:
Since we have 2 choices for each digit (1 or 2), the total number of 5-digit numbers that can be formed is given by 2 * 2 * 2 * 2 * 2 = 32. This means there are 32 possible 5-digit numbers using only the digits 1 and 2.
2. Counting the number of 5-digit numbers where all digits are the same:
If all the digits are the same, there can only be two possibilities: 11111 or 22222. So, there are only 2 such numbers.
3. Counting the number of 5-digit numbers where at least one digit is different:
To find the number of 5-digit numbers where at least one digit is different, we need to subtract the number of numbers where all digits are the same from the total number of 5-digit numbers.
Number of 5-digit numbers where at least one digit is different = Total number of 5-digit numbers - Number of 5-digit numbers where all digits are the same
= 32 - 2
= 30
Therefore, the correct answer is option 'A', 30.
1. Counting the total number of 5-digit numbers:
Since we have 2 choices for each digit (1 or 2), the total number of 5-digit numbers that can be formed is given by 2 * 2 * 2 * 2 * 2 = 32. This means there are 32 possible 5-digit numbers using only the digits 1 and 2.
2. Counting the number of 5-digit numbers where all digits are the same:
If all the digits are the same, there can only be two possibilities: 11111 or 22222. So, there are only 2 such numbers.
3. Counting the number of 5-digit numbers where at least one digit is different:
To find the number of 5-digit numbers where at least one digit is different, we need to subtract the number of numbers where all digits are the same from the total number of 5-digit numbers.
Number of 5-digit numbers where at least one digit is different = Total number of 5-digit numbers - Number of 5-digit numbers where all digits are the same
= 32 - 2
= 30
Therefore, the correct answer is option 'A', 30.
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Community Answer
The number of 5-digit numbers that can be made using the digits 1 and ...
Total number of numbers without restriction 25.
Two numbers have all the digits equal. So, the required number of numbers = 25 - 2
Two numbers have all the digits equal. So, the required number of numbers = 25 - 2
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The number of 5-digit numbers that can be made using the digits 1 and 2 and in which at least one digit is different, isa)30b)31c)32d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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