2022 Stat 1 Permutations and Combinations -BMQ Solutions (RVHS)

H2 Mathematics (9758) River Valley High School, Mathematics Department, 2022 1 Statistics Tutorial 1: Permutations and Combinations Basic Mastery Questions 1. There are two bags. The first bag co ntains balls numbered 1 to 40 , the second contains balls numbered 1 to 10. (a) How many ways could one ball be chosen? 40 + 10 = 50 (b) How many ways could one ball be chosen from each bag? 40 × 10 = 400 (c) Considering only the bag with balls numbered 1 to 40: (i) How many ways could all 40 balls be arranged in a straight line? 40! (ii) How many ways could 3 balls be drawn from the bag, if the balls are returned to the bag after each draw, and the order matters? 40 × 40 × 40 = 403 = 64 000 (iii) How man y ways could 6 balls be drawn fr om the bag, if the balls are not replaced, and the order matters? 𝑃6 40 = 40! 34! = 2 763 633 600 (iv) How many ways could 10 balls be drawn from the bag such that the first and last balls are even, if the balls are not replaced and the order matters? 20 × 19 × 𝑃8 38 = 147.49 10 (3sf) (d) How many ways could 6 balls be drawn from the first bag, and 1 ball be drawn from the second bag if the balls are drawn without replacement, and the order of the draw does not matter? (40 6 ) (10 1 ) = 38 383 800 2. J74/P1/1 Four men, two women and a child sit at a round table. Find the number of ways of arranging the seven people if the child is seated (a) between the two women (b) between two men. (i) 4!2! = 48 (ii) 4 4!2! 2882  