The problem discusses the number of ways to choose a pair of distinct numbers \(a\) and \(b\) from the set \{1, 2, 3, ..., 49\} such that \(|a - b| \leq 3\). The correct answer is 141, derived from the formula \(49 \times 3 - 6\). The discussion clarifies that distinct pairs are considered unordered, meaning \([41, 42]\) is the same as \([42, 41]\). This distinction is crucial for accurately counting the pairs.
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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?