8. Consider the diagram B a) How many pathways from A to B are possible, moving only down or to the right? b) How many pathways from A to C are possible moving only down or to the right? Explain using permutations and the fundamental couting principle. 9 . Solve for n. a) nP3 = 120 b) 3(n C2) = 12(n C1) 10. Expand (y - 2) using the binomial theorem. Simplify your answer. 11. How many ways can all the letters of aloha be arranged if a) The 'a's must be together? b) The 'a's cannot be together? C) Each arrangement must begin with a vowel and the consonants cannot be together?Permutations and Combinations 1. How many three-digit numbers with no repeating digits can be formed using the digits 0, 1, 2, 8, and 9? a) 100 b ) 60 C ) 48 d) 125 2. In how many ways can the letters of the word SWEEPERS be arranged in a row? a) 40 320 b ) 20 160 C ) 6720 d) 3360 3 How many five member committees containing two Conservatives, two New Democrats, and one Liberal can be formed from seven Conservatives, six New Democrats, and five Liberals? a) 6300 b ) 3150 C) 1575 d) 8568 4. How many terms are in the expansion of (2x - 5y2)11? a) 13 b ) 12 C ) 11 d) 10 5. What is a simplified expression for the third term in the expansion of (2x2 + 3y)?? a) 6048x10 2 b) 9072x8y3 c) 12 096x10 y2 d) 15 120x8y3 6. The numbers 1 6 15 20 15 6 1 represent the seventh row in Pascal's Triangle. What is the sixth number in the next row? a) 1 b ) 7 C ) 21 . d) 35 7. For six multiple choice questions, two answers are A, two answers are B, one answer is C, and one answer is D. a) How many answer keys are possible? b ) List the possible answer keys if you know the answers to questions 3 and 5 are C and D, respectively