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Q.

In a tournament there are sixteen players  S1,S2........S16  and divided into eight pairs at random from each game a winner is decided on the basis of a game played between the two players of the pair. Assuming that  all the players have equal strength

 Column-I Column-II
A)The probability that  S1 is one of the winnerp)815
B)The probability that exactly one of  S1  or S2  is a winnerq)12
C)Both S1 and  S2 are among eight winnersr)730
D)Both S1 and  S2 are not among eight winnerss)1240

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a

A-q, B-p, C-r, D-r

b

A-q, B-p, C-r, D-s

c

A-p, B-q, C-r, D-s

d

None

answer is A.

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Detailed Solution

A) P ( S1 and 7 other win) =(15C7)(16C7)   [ All the players are of equal strength] =[(15C7)168×(16C7)]=12
B) P(only one of S1,S2 and 7 others win)
 =(2C1×14C1)(16C8)=(14C7)(15C7)=1477×7815=815
C) P(Both S1,S2 and 6 others win)
=(2C2×14C6)(16C8)=1468×8816=730
D) P(8 winners are among rest of 14 players
=(14C6)(16C8)=148.6×8816=730

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