Number of ways to choose a pair of distinct number

[songoku]

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

 

[Andrew Mason]

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

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

 

[songoku]

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

If the question asks for "ordered pair" then [41,42] is different from [42, 41]?

Thanks

 

[Delta2]

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?

 

[Andrew Mason]

If the question asks for "ordered pair" then [41,42] is different from [42, 41]?

Thanks

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}.

AM

 

[songoku]

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?

I am not required to do any programming right now so I don't know what program to use because I have not learned any.Thank you very much for the help AM and delta2