Answer:
The number of possible choices of my team and the opponents team is
 [tex]\left\begin{array}{ccc}n-1\\E\\n=1\end{array}\right i^{3}[/tex]
Step-by-step explanation:
selecting the first team from n people we have [tex]\left(\begin{array}{ccc}n\\1\\\end{array}\right) = n[/tex] possibility and choosing second team from the rest of n-1 people we have [tex]\left(\begin{array}{ccc}n-1\\1\\\end{array}\right) = n-1[/tex]
As { A, B} = {B , A}
Therefore, the total possibility is [tex]\frac{n(n-1)}{2}[/tex]
Since our choices are allowed to overlap, the second team is [tex]\frac{n(n-1)}{2}[/tex]
Possibility of choosing both teams will be
[tex]\frac{n(n-1)}{2} * \frac{n(n-1)}{2} \\\\= [\frac{n(n-1)}{2}] ^{2}[/tex]
We now have the formula
1³ + 2³ + ........... + n³ =[tex][\frac{n(n+1)}{2}] ^{2}[/tex]
1³ + 2³ + ............ + (n-1)³ = [tex][x^{2} \frac{n(n-1)}{2}] ^{2}[/tex]
=[tex]\left[\begin{array}{ccc}n-1\\E\\i=1\end{array}\right] = [\frac{n(n-1)}{2}]^{3}[/tex]
