Podcast
Questions and Answers
What is the formula for calculating the sum of the numbers formed by taking all the given n digits excluding 0?
What is the formula for calculating the sum of the numbers formed by taking all the given n digits excluding 0?
- (Sum of all the n digits) × (n-1)! × (10^n)
- (Sum of all the n digits) × (n-1)! × (111... n times) (correct)
- (Sum of all the n digits) × (n!) × (111... n times)
- (Sum of all the n digits) × (n-2)! × (111... n times)
How is the sum of the numbers formed by n digits including 0 calculated?
How is the sum of the numbers formed by n digits including 0 calculated?
- (Sum of all the n digits) × [(n-1)! × (111... n times)]
- (Sum of all the n digits) × [(n)! × (111... (n-1) times)]
- (Sum of all the n digits) × [(n-1)! × (111... n times) - (n-2)! (111... (n-1) times)] (correct)
- (Sum of all the n digits) × [(n-1)! × (10^n)]
For r digited numbers formed using n non-zero digits, what is the correct formula for their sum?
For r digited numbers formed using n non-zero digits, what is the correct formula for their sum?
- (n!) × (sum of n digits) × (111... (r times))
- (n^r) × (sum of all n digits) × (111... (r times)) (correct)
- (n^r) × (sum of all n digits) × (10^{(r-1)})
- (n^r) × (sum of all digits) × (10^r)
What is the modified formula for the sum of r digited numbers using n digits including zero?
What is the modified formula for the sum of r digited numbers using n digits including zero?
What formula calculates the sum of digits in the units place of n digited numbers formed by non-zero digits?
What formula calculates the sum of digits in the units place of n digited numbers formed by non-zero digits?
How is the value of digits in the 100's place calculated for n digited numbers formed with non-zero digits?
How is the value of digits in the 100's place calculated for n digited numbers formed with non-zero digits?
What effect does excluding zero have when calculating the sum of all r digited numbers formed from n digits?
What effect does excluding zero have when calculating the sum of all r digited numbers formed from n digits?
In the formula for the sum of digits in any position of all numbers formed with n digits, what does (n-1)! represent?
In the formula for the sum of digits in any position of all numbers formed with n digits, what does (n-1)! represent?
Which of the following is NOT included in the formula for the sum of r digited numbers formed with the n digits including zero?
Which of the following is NOT included in the formula for the sum of r digited numbers formed with the n digits including zero?
Flashcards
Sum of numbers formed using all digits (excluding 0)
Sum of numbers formed using all digits (excluding 0)
The sum of all the numbers formed by taking all the given 'n' digits (excluding 0) is calculated as: (Sum of all the 'n' digits) × (n-1)! × (111... 'n' times).
Sum of numbers formed using all digits (including 0)
Sum of numbers formed using all digits (including 0)
The sum of all the numbers formed by taking all the given 'n' digits (including 0) is calculated as: (Sum of all the 'n' digits) × [(n-1)! × (111... 'n' times) - (n-2)! (111... (n-1) times)]
Sum of 'r' digit numbers (non-zero digits)
Sum of 'r' digit numbers (non-zero digits)
The sum of the 'r' digited numbers that can be formed using the given 'n' non-zero digits is: nr × (sum of all 'n' digits) × 111... (r times)
Sum of 'r' digit numbers (including zero)
Sum of 'r' digit numbers (including zero)
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Sum of digits in any place
Sum of digits in any place
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Sum of units place digits (non-zero)
Sum of units place digits (non-zero)
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Sum of hundreds place digits (non-zero)
Sum of hundreds place digits (non-zero)
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Study Notes
Permutations and Combinations
- Permutations of 'n' different things taken all at a time: n!
- Circular permutations of 'n' different things: (n-1)!
- Permutations of 'n' different things taken 'r' at a time: P(n,r) = n!/(n-r)!
- Combinations of 'n' distinct objects taken 'r' at a time: C(n,r) = n!/(r! (n-r)!)
- Combinations of 'n' distinct objects taken 'r’ at a time, where k particular objects always occur: C(n-k,r-k)
- Combinations of 'n' distinct objects taken 'r' at a time, where k objects never occur: C(n-k,r)
Sum of Numbers Formed from Digits
- Sum of numbers formed by taking all given n digits (excluding 0): (Sum of all digits) * (n-1)! * (111... (n-times))
- Sum of numbers formed by taking all given n digits (including 0): (Sum of all digits) * [( (n-1)! * (111... (n times)))-( (n-1)! *(111... (n-1 times)))]
- Sum of 'r' digit numbers formed using n non-zero digits (r ≤ n): (Sum of all digits) * (111..r times) * P(n,r)
- Sum of 'r' digit numbers formed using n digits (including zero): (Sum of digits) * 111... (r times) * P(n,r)
- Sum of digits in any place of numbers formed from n digits(excluding 0) : (n-1)! * (sum of digits)
- Sum of digits in a specific place of n digited numbers: (n-1)! * (Sum of the digits) * [value of place position in units, 100s etc]
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Description
Test your knowledge on permutations and combinations with this engaging quiz. Explore concepts like circular permutations and the sum of numbers formed by digits. Perfect for students looking to reinforce their understanding of this fundamental topic in mathematics.
