SOLUTION: Triplet X,Y,Z are chosen from the set {1,2,3,.....24,25} such that X grater equal to Y and Y equal to Z.How many such triplets are possible?

Question 1135369: Triplet X,Y,Z are chosen from the set {1,2,3,.....24,25} such that X grater equal to Y and Y equal to Z.How many such triplets are possible?
Answer by ikleyn(52785) (Show Source): You can put this solution on YOUR website!
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Since in each triplet (X,Y,Z), the values Y and Z are equal, according to the condition,
you may forget about triplets and reformulate your problem EQUIVALENTLY in this much simpler way:

        Doublets (X,Y) are chosen from the set {1,2,3,.....24,25} such that 
        X >= Y. How many such doublets are possible?

Solution

For Y = 1,  there are  25 such doublets  (1,1), (2,1), (3,1), . . . , (25,1).


For Y = 2,  there are  24 such doublets         (2,2), (3,2), . . . , (25,2).


For Y = 3,  there are  23 such doublets                (3,3), . . . , (25,3).



. . . . . . . .  And so on  . . . . . 


Finally, for Y = 25,  there is ONLY ONE such doublet                  (25,25).



So, the answer to your question is the value of the sum  25 + 24 + 23 + . . . + 1.


This value is very well known: it is the sum of the arithmetic progression

    1 + 2 + 3 + . . . + 25 =  = 325.


ANSWER.  The number of such triplets is 325.

Solved.

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