Instructions: 1. Do not write solutions on the question page 2. Give your answers in exact forms. & In order to receive credits, you must show your work. Do not do computations in your head. lustead, write them out on the exam paper. 4. Place a box around YOUR FINAL ANSWER) to each question. Name and Surname: 1. (80 points) Counting A. A committee of 6 people is to be chosen from a group consistius of 7 men and s women. If the committee must consist of at least 2 women and at least S men, how many different coxittees are possible? B. How many different letter configurations of leugth 4 or 5 can be formed using the letters of the word REALIZE? 2. (20 points) Probability A. Two numbers from 1 to 10 are selected randomly in succession. What is the probability that their product is less than or equal to 49? B. If'a die is rolled 5 times, what is the probability that 5 comes up at least once? 3 (20 points) Conditional Probability A. Three cards are randomly selected, without replacement, from an ordinary deck of 52 playigg cards. Compute the conditional probability that the first card selected is an ACE given that the second and third cards are ACES. B. If P(EnE) = 0.144. P(EIF) = 0.86, and P(FIE) = 0.4, then (a) P(E) =? (b) P(P)=? (e) P(EUF) =? (d) Are the events E and F independent