find the orthogonal decomposition of v with respect to W

Week1 11.3-11.4 Combinations, Fundamentals of Probability Spring 2016 Permutation vs Combination Permutation Combination Order MATTERS!! DOES NOT MATTER Formula n ! nP r n ! nPr▯ nCr▯ ▯ ▯n▯r ! r ! r ! n▯r ! Permutation or Combination 1. How many different 4-letter passwords can be formed from the letters A, B, C, D, E, F, and G if no repetition of letters is allowed 2. 50 people purchase raffle tickets. 3 winning tickets are selected at random. In how many different ways can the prizes be awarded Example 1 A 4-person committee is to be chosen from a group of 7 students. How many different committees could be formed Q: How did we get the formula for combination A: Let’s illustrate this with an example – Example 2 Suppose we have 4 letters A, B, C, and D. The number of permutations of these 4 letters taken 3 at a time is 1 The permutations are: There are combinations. Number of permutations = Number of combinations Example 3 There are 13 children on a playground, 8 boys and 5 girls. a. Determine the number of ways to select 7 from them. b. Find the number of ways to select 7, if 4 are boys and 3 are gi