Math 141H-copyright Joe Kahlig, 10C Page 1Section 6.3: The Multiplication PrincipleAn experiment is to flip a coin. How many outcomes are possible if the coin is flippedA) Twice. S = { HH, HT, TH, TT}B) Three times. S = { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}C) Five times.Example: An experiment is to draw two letters in succession from a box that has an A, B, and C.How many outcomes are th ere?Definition - Multiplication Principle: An outcome consists of k successive selections with nichoices for the i-th selection. The th e total number of outcomes isExample: There are 6 roads from town A to town B and 7 roads from town B to town C. How manyways can you go from town A to town C?Example: How many ways can you select a president, vice-president and secretary from a group of 10people?Definition: A factorial, n!, is the pro duct of integers from n down to 1. For example: 5! = 5∗4∗3∗2∗1.By definition, 0! = 1Example: Compute the follow ing.A) 10! B) 14!Math 141H-copyright Joe Kahlig, 10C Page 2Example: How many three digit numbers can be f ormed from the digits: 2, 3, 4, 5, 6, 7, 8?A) No restrictions.B) The number is even.C) The digits are even.D) The number is even and no digit is repeated.Example: Five boys and five girls are to be seated in a row. Find how many ways can this be done ifA) no restrictions.B) they alternate seats.C) girls sit together and boys sit together.D) girls sit together.E) Sue, Jill, or Sarah are seated in the end seats.Math 141H-copyright Joe Kahlig, 10C Page 3Example: How many 3 digit numbers haveA) none of the digits are a 7.B) Exactly one digit a 7.C) Exactly two digit being a 7.D) Exactly three digits a 7.E) no digits repeated and the number is even.Example: How many 5 digit numbers have at least one digit being a 7?Example: A computer code is to be constructed with either 5 letters or 2 letters followed by thr eedigits. How many codes are possible if no letters may be repeated in the code.Example: Four couples are to seated in a row. How many ways can this be done if the couples are tobe seated together?Example: An ATM code contains 4 digits. How many codes are possible if the ban k will not allowthe codes to have all the same
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