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The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is.?
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The number of numbers lying between 100 and 1000 can be formed with th...
Counting the Numbers between 100 and 1000 with Digits 1-7
In order to count the number of numbers between 100 and 1000 that can be formed with the digits 1-7, we will need to use the concepts of permutation and combination. Permutation is used when the order of the digits matters, while combination is used when the order does not matter.
Using Permutation
If we use permutation, we will need to find out how many different arrangements of three digits we can make using the digits 1-7. We can use the formula for permutation:
nPr = n! / (n - r)!
where n is the total number of objects and r is the number of objects that we want to arrange in a specific order.
In this case, we have 7 digits to choose from, and we want to arrange them in groups of 3. Therefore:
7P3 = 7! / (7 - 3)! = 7! / 4! = 210
This means that there are 210 different arrangements of three digits that we can make using the digits 1-7. However, not all of these arrangements will be between 100 and 1000.
Using Combination
Since we are looking for numbers between 100 and 1000, we know that the first digit must be either 1, 2, or 3. We can use combination to find out how many different combinations of the remaining two digits we can make using the digits 1-7.
The formula for combination is:
nCr = n! / r!(n - r)!
where n is the total number of objects, r is the number of objects we want to choose, and (n - r) is the number of objects that we do not want to choose.
Since we are choosing 2 digits from a set of 7, we can use the formula:
7C2 = 7! / 2!(7 - 2)! = 7! / 2!5! = 21
This means that there are 21 different combinations of two digits that we can make using the digits 1-7.
Multiplying the Results
To find out how many numbers between 100 and 1000 we can make using the digits 1-7, we need to multiply the number of arrangements of three digits by the number of combinations of two digits:
210 x 21 = 4,410
Therefore, there are 4,410 numbers between 100 and 1000 that can be formed with the digits 1-7.
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The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is.?
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The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is.? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is.?.
The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is.? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3,4,5,6,7 is.?.
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