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The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is
- a)98
- b)72
- c)90
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The figures 4, 5, 6, 7, 8 are written in every possible order. The num...
There are in total 6 numbers, 4,5,6,7,8.
Now consider the number 56000
Consider the numbers of the form
56−−−.
Considering no repetitions we get
3×2×1 = 6 numbers.
Similarly for 57−−− and 58−−−.
Hence 3×6 = 18 numbers.
Now consider the numbers starting with 6.
6−−−−
We get 4×3×2×1 = 24.
Similarly for the numbers starting with 7 and 8 we get in total 24 numbers each.
Hence total number of numbers greater than 56000 will be
= (24×3)+18
= 72+18 = 90
Now consider the number 56000
Consider the numbers of the form
56−−−.
Considering no repetitions we get
3×2×1 = 6 numbers.
Similarly for 57−−− and 58−−−.
Hence 3×6 = 18 numbers.
Now consider the numbers starting with 6.
6−−−−
We get 4×3×2×1 = 24.
Similarly for the numbers starting with 7 and 8 we get in total 24 numbers each.
Hence total number of numbers greater than 56000 will be
= (24×3)+18
= 72+18 = 90
Most Upvoted Answer
The figures 4, 5, 6, 7, 8 are written in every possible order. The num...
To find the number of numbers greater than 56000 that can be formed using the digits 4, 5, 6, 7, and 8, we need to consider all possible permutations of these digits and count the numbers that satisfy the given condition.
We can start by analyzing the possible positions of each digit in the number.
1. Thousands place:
Since the number has to be greater than 56000, the digit in the thousands place must be either 6, 7, or 8. So, there are three options for the thousands place.
2. Hundreds place:
Once we have selected a digit for the thousands place, we have four remaining digits (4, 5, 7, and 8) to choose from for the hundreds place. However, we need to ensure that the number remains greater than 56000. If the digit in the thousands place is 6 or 7, we can choose any of the remaining four digits for the hundreds place. But if the digit in the thousands place is 8, we can only choose from the remaining three digits (4, 5, and 7) for the hundreds place.
3. Tens place:
After selecting a digit for the thousands and hundreds places, we have three remaining digits (4, 5, and 8 if the thousands place digit is 6 or 7; 4, 5, and 7 if the thousands place digit is 8) to choose from for the tens place. Again, we need to ensure that the number remains greater than 56000.
4. Units place:
Finally, after selecting digits for the thousands, hundreds, and tens places, we are left with two remaining digits (4 and 5 if the thousands place digit is 6 or 7; 4 and 5 if the thousands place digit is 8) to choose from for the units place.
Now, we can calculate the total number of numbers that satisfy the given condition by multiplying the number of options for each place value:
Number of options for the thousands place: 3
Number of options for the hundreds place: 4 (if the thousands place digit is 6 or 7), 3 (if the thousands place digit is 8)
Number of options for the tens place: 3
Number of options for the units place: 2
Total number of numbers = (3) * (4 + 3) * (3) * (2) = 90
Therefore, the correct answer is option C: 90.
We can start by analyzing the possible positions of each digit in the number.
1. Thousands place:
Since the number has to be greater than 56000, the digit in the thousands place must be either 6, 7, or 8. So, there are three options for the thousands place.
2. Hundreds place:
Once we have selected a digit for the thousands place, we have four remaining digits (4, 5, 7, and 8) to choose from for the hundreds place. However, we need to ensure that the number remains greater than 56000. If the digit in the thousands place is 6 or 7, we can choose any of the remaining four digits for the hundreds place. But if the digit in the thousands place is 8, we can only choose from the remaining three digits (4, 5, and 7) for the hundreds place.
3. Tens place:
After selecting a digit for the thousands and hundreds places, we have three remaining digits (4, 5, and 8 if the thousands place digit is 6 or 7; 4, 5, and 7 if the thousands place digit is 8) to choose from for the tens place. Again, we need to ensure that the number remains greater than 56000.
4. Units place:
Finally, after selecting digits for the thousands, hundreds, and tens places, we are left with two remaining digits (4 and 5 if the thousands place digit is 6 or 7; 4 and 5 if the thousands place digit is 8) to choose from for the units place.
Now, we can calculate the total number of numbers that satisfy the given condition by multiplying the number of options for each place value:
Number of options for the thousands place: 3
Number of options for the hundreds place: 4 (if the thousands place digit is 6 or 7), 3 (if the thousands place digit is 8)
Number of options for the tens place: 3
Number of options for the units place: 2
Total number of numbers = (3) * (4 + 3) * (3) * (2) = 90
Therefore, the correct answer is option C: 90.
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Community Answer
The figures 4, 5, 6, 7, 8 are written in every possible order. The num...
It's about permutation and combination
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The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 isa)98b)72c)90d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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