Please answer all numbers and show complete solutions, thank you!

Problem 11: In how many ways can a panel of5judges make a majority decision? A. 16 C. 60 B. 20 D. 120 Problem 12: Howr many different ways can 3 red, 4 yellow, and 2 blue bulbs be arranged in a string of Christmas tree lights with 9 sockets? A. 1540 C. 1820 B. 1430 D. 1260 Problem 13: The CIT U CE department has 15 faculty members. Four are to be selected to attend the CE convention. How many ways can the school select the 4 member if 2 of them are best friends and may or may not attend together? A. 720 C. 793 B. 144 D. 844 Problem 14: From ? men and 5 women, a committee of four is chosen by lot. What is the probability that the committee will involve all men or all women? A. 11l'09 C. YlQQ B. 1(99 D. 8(99 Problem 15: The probability that the wife will be alive in 20 years is 0.8 and the probability that the husband will be alive in 20 years is 0.70. What is the probability that at least one of them will be alive in 20 years? A. 0.06 C. 0.94 B. 0.45 D. 0.50