# Probability in knock-out torunament

1. Mar 20, 2009

### chrisyuen

1. The problem statement, all variables and given/known data

Albert, Bobby and six other players take part in a table-tennis knock-out tournament. The winner of each match can proceed to the next round as shown in the following figure and the loser is knocked out. The players are randomly assigned to the eight positions in the first round. Suppose the eight players are equally skillful.

(a) What is the probability that Albert will play Bobby in the first round?

(b) What is the probability that Albert will ever play Bobby in a match during a tournament?

(a) $$\frac{1}{7}$$
(b) $$\frac{1}{4}$$)

2. Relevant equations

Permutation and Combination Formulae

3. The attempt at a solution

Part (a), total combinations = $$\frac{8!}{6!}$$ = 56

P = $$\frac{8}{56}$$ = $$\frac{1}{7}$$.

Am I correct?

Part (b), I don't know how can I start this part.

Can anyone tell me how to solve it?

Thank you very much!

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