Arrangement of Tokens in 2 identical Boxes

There are n number of tokens marked 1,2,3,4,..........n respectively.
One has to pick up 2 tokens and put them in 2 boxes, one in each.
None of the boxes should  remain empty nor have more than 1 token.
Both the boxes are identical.
In how many ways, 2 tokens can be allocated to both boxes out of n available tokens ? Ans : C(n,2)
What is the minimum sum of 2 tokens so allocated ? Ans - 1+2=3
What is the maximum sum of 2 tokens so allocated ? Ans:- n+(n-1) = 2n-1
What is the average sum of 2 tokens so allocated ? xav=[3+(2n-1)] /2 = n+1
In how many ways, the 2 tokens can be arranged so as to get the average sum? Ans:-quotient (n/2)
If X is the sum of 2 tokens such that X=xav ±x, then no. of arrangements to get X is same for  xav+x & xav-x.
If n is odd, no. of arrangements to get a number equal to  xav ±1=No. of arrangements to get xav
If n is even, no. of arrangements to get a number equal to  xav ±1=(No. of arrangements to get xav) -1.
Example-- No. of tokens 1,2,3,.......8. One token in each of 2 boxes. Minimum no. that can be put--3, maximum no. that can be put--15, Average no. --09
Token with   sum-3(xav-6)           sum-4(xav-5)      sum-5(xav-4)       sum-6(xav-3)        sum-7(xav-2)        sum-8(xav-1)          sum-9 (xav=9+x=0)
                            1+2                          1+3                       1+4                     1+5                      1+6                      1+7                         1+8

                                                                                          2+3                    2+4                      2+5                       2+6                         2+7

                                                                                                                                                3+4                       3+5                         3+6


                sum-10(xav+1)     sum-11(xav+2)    sum-12 (xav+3)    sum-13(xav+4)      sum-14(xav+5)     sum-15(xav+6)
                        2+8                       3+8                        4+8                       5+8                         6+8                     7+8

                        3+7                       4+7                        5+7                      6+7

                        4+6                      5+6



No. of tokens
Sum of tokens in 2 boxes is
no. of boxes
no. of ways total no. of  tokens can be allocated in 2 boxes
Minimum value of sum
Maximum value of sum
Average value of sum
no. of ways of allocation of 2 tokens to get average sum
no. of different arrangements to get the sum as above