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Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in 2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the group. The top two teams from each group enter the semi finals ( after which the winner is decided by knockout). However, Paul has a soft spot for India and when India plays any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world cup?
(a) (2/3)^10 (b) (2/3)^9 + 8/3 * (2/3)^9
(c) 8/3 * (2/3)^9 (d) (2/3)^10 + 8/3*(2/3)^9

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TCS Other Question
A lady had fine gloves and hats. 25 blue, 7 red and 9 gey. She had to select a pair among them. But there was no light so she had to select in darkness the correct pair with a glove and a hat. Therefore how many combinations of same color she can select? A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says 'At least n of the statements on this sheet are false.' Which statements are true and which are false?

a) The even numbered statements are true and the odd numbered are false.
b) The odd numbered statements are true and the even numbered are false.
c) The first 35 statements are true and the last 35 are false.
d) The first 35 statements are false and the last 35 are false.