The problem involves determining the number of ways to choose a pair of distinct numbers from the set {1, 2, 3, ...49} under the condition that the absolute difference between the two numbers is less than or equal to 3.
Participants are exploring the implications of the term "distinct" in the context of the problem, with some suggesting that the question could have been clearer. A formula has been proposed by one participant, and there is an ongoing discussion about how to approach the counting problem, including considerations for programming.
There is some confusion regarding the terminology used in the problem statement, particularly around the distinction between ordered and unordered pairs. Participants are also noting that they are not required to use programming for this problem, which may limit their exploration of potential solutions.
I would say that because the question asks for "distinct" pairs, order does not matter. So [42,41] is not distinct from [41,42].songoku said:Homework Statement
The number of ways to choose a pair of distinct numbers a and b from the set {1, 2, 3, ...49} such that |a - b| ≤ 3 is
a. 141
b. 144
c. 147
d. 150
e. none of the above
Homework Equations
not sure
The Attempt at a Solution
Is a = 41 and b = 42 considered the same as a = 42 or b = 41? Or they are two different cases?
Thanks
If the question asks for "ordered pair" then [41,42] is different from [42, 41]?Andrew Mason said:I would say that because the question asks for "distinct" pairs, order does not matter. So [42,41] is not distinct from [41,42].
AM
A distinct pair would be any two-element subset of the given set, ie. a and b being distinct elements in that set. Since the question merely asked for distinct pairs without referring to them as "ordered", then it would appear that order does not matter. The question should have asked for distinct unordered pairs to avoid confusion. So, yes, if the question had asked for distinct ordered pairs then {41,42} would be different than {42,41}.songoku said:If the question asks for "ordered pair" then [41,42] is different from [42, 41]?
Thanks
Delta2 said:I think the correct answer is 49x3-6=141
The way I wrote it 49x3-6 might help you to find the algorithm that will do the counting for this problem. I think if you had to write a computer program to do the counting, what program would you do?