A permutation and combination problem

In summary, the number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41), and (41, 0) is less than 41. To count the points in the triangle, you can consider a region for which the number of internal points is easier to count and has a straightforward relationship with the internal point count of the triangle.
  • #1
vijayramakrishnan
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.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is

(1) 901 (2) 861 (3) 820 (4) 780

my attempt:
for this to be true i know that sum of x and y coordinate should be 41 but i don't know how to proceed.
 
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  • #2
vijayramakrishnan said:
for this to be true i know that sum of x and y coordinate should be 41 but i don't know how to proceed.
No, the sum must be less than or equal to 41. How would you count the points in that triangle?
 
  • #3
andrewkirk said:
No, the sum must be less than or equal to 41. How would you count the points in that triangle?
yes it should be less than 41,changed.sorry
 
  • #4
vijayramakrishnan said:
yes it should be less than 41,changed.sorry
Yes, less than, not less or equal. Likewise what are the minimum x and y values?
To solve the question, can you think of a region for which:
- the number internal points is much easier to count, and
- there is a fairly straightforward relationship between its internal point count and that of your triangle?
 

1. What is a permutation and combination problem?

A permutation and combination problem is a type of mathematical problem that involves counting the number of ways to arrange or select items from a given set. Permutations refer to the arrangement of items in a specific order, while combinations refer to the selection of items without regard to order.

2. What is the difference between permutations and combinations?

The main difference between permutations and combinations is that permutations take into account the order of the items, while combinations do not. For example, the permutations of the letters "ABC" would include "ABC", "ACB", "BAC", etc., while the combinations would only include "ABC".

3. How do I calculate permutations and combinations?

To calculate permutations, you would use the formula nPr = n!/(n-r)!, where n is the total number of items and r is the number of items being selected. For combinations, you would use the formula nCr = n!/r!(n-r)!. In both cases, the exclamation point (!) represents the factorial function, which means multiplying a number by all the numbers below it.

4. What are some real-life applications of permutation and combination problems?

Permutation and combination problems can be found in various fields, including mathematics, computer science, and statistics. They are often used in cryptography, where the order of letters or numbers in a code is important. They also have applications in genetics, gambling, and sports scheduling.

5. Can you give an example of a permutation and combination problem?

Sure, here's a classic example: In how many ways can a group of 4 people be chosen from a group of 10? The answer would be 10C4 = 10!/(4!(10-4)!) = 10!/4!6! = 210. This means there are 210 different combinations of 4 people that can be chosen from a group of 10.

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