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The factorial of a nonnegative integer n is written n! (pronounced “n factorial”) and is defined as follows: n! = n · (n - 1) · (n - 2) · … · 1 (for values of n greater than to 1) and n! = 1 (for n = 0 or n = 1). For example, 5! = 5 · 4 · 3 · 2 · 1, which is 120. Use while structures in each of the following: a) Write a program that reads a nonnegative integer and computes and prints its factorial. Use the following function prototype to calculate factorial: int myFactorial(int n); b) Write a program that estimates the value of the mathematical constant e by using the formula: Use the following function prototype to calculate e: double myE( ); Hint: Use an accuracy of 10 terms. c) Write a program that computes the value of ex by using the formula Use the following function prototype to calculate e: double myEx(int x);
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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?
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