Probable chances in life #3

Probability Level 3

$40$ teams play in a tournament. Each team plays every other team just once. Each game results in a win for one team. If each team has a $50\%$ chance of winning each game ,the probability that at the end of the tournament every team has won a different number of games is :-

\dfrac{40!}{2^{780}}

\dfrac{40!}{780}

\dfrac{1}{780}

\dfrac{40!}{3^{780}}

1 solution

Parag Zode
Dec 22, 2014

Here ,we see that the team totals must be 0 ,1 ,2 ,3 ,...,39.

Let the teams be $T_1,T_2,T_3,...T_{40}$ so that $T_i$ loses to $T_j$ for $i<j$ . This implies that the order itself uniquely determines the result of every game. There are $40!$ such orders and $780$ games so total possible outcomes of the game are $2^{780}$ . Hence the probability is $\dfrac{40!}{2^{780}}$

Probable chances in life #3

1 solution

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