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1. A man has eight shirts, four pairs of pants, and five pairs of shoes. How many different outfits are possible? 2. How many times
1. A man has eight shirts, four pairs of pants, and five pairs of shoes. How many different outfits are possible? 2. How many times are the print statements executed? For i = 1 to m printIn(i) For j =1 to n printin(j) 3. How many times is the print statement executed? for i = 1 to m for j = 1 to n printIn(i,j)10. Suppose we have an experiment where a coin is flipped and a die is rolled and the result of the coin flip and die roll is noted. a. What is the sample space? b. Define an event A as the coin shows a head and the die show an even number. List the elements of the event A. . Define an event B as the die shows an odd number. List the elements of event B. d. Define an event C as the coin shows a head and the die shows a number less than 4. List the elements of event C. 11. Acard is selected at random from an ordinary 52 card deck. a. What is the probability that the card is the ace of spades? b. What is the probability that the card selected is a jack? c. What is the probability that the card is a heart? 12. Two fair die are rolled. a. What is the probability that the sum of the numbers showing on the dice is a 97 b. What is the probability that the sum of the numbers showing on the dice is odd? c. What is the probability of doubles? 13. Six microprocessors are randomly selected from a lot of 100 microprocessors among which 10 are defective. Find the probability of obtaining no defective microprocessors. 14. If a coin is flipped 10 times what is the probability of no heads? 15. If a coin is flipped 10 times what is the probability of at least one head? 16. If a coin is flipped 10 times what is the probability of approximately 5 heads, that is, exactly 4 or 5 or 6 heads? 17. If a coin is flipped 10 times what is the probability of approximately 5 heads, that is, exactly 4 or 5 or 6 heads given at least one head? 18. Find the coefficient of the 5% term when the expression (25 -)"is expanded. 19. Expand (x+ v) using the binomial theorem. 20.Prove that among a group of six students, at least two received the same grade on the final exam. ( The grades assigned were chosen from A, B, C,D, F) 4. How many eight-bit strings read the same from either end? (An example of such an eight-bit string is 01111110. Such strings are called palindromes.) 5. How many permutations are there of 11 distinct objects? 6. How many 5-permutations are there of 11 distinct objects? 7. In how many ways can we select a committee of four from a group of 12 persons? 8. In how many ways can five distinct Martians and eight distinct Jovians be seated at a circular table if no two Martians sit together. 9. Suppose we have a set of 50 microprocessors of which four are defective. a. In how many ways can we select a set of four microprocessors? b. In how many ways can we select a set of four non-defective microprocessors? c. In how many ways can we select a set of four microprocessors containing exactly two defective microprocessors? d. In how many ways can we select a set of four microprocessors containing at least one defective microprocessor
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