Problem 18
Question
Eight people are boarding an aircraft. Two have tickets for first class and board before those in the economy class. In how many ways can the eight people board the aircraft?
Step-by-Step Solution
Verified Answer
The total number of ways the eight people can board the aircraft is \(2!*6! = 14560\).
1Step 1: Calculate the possible orders of the first-class passengers
The first-class passengers can board in \(2!\) ways. This is calculated by using the factorial function: \(2! = 2 * 1\).
2Step 2: Calculate the possible orders of the economy class passengers
The economy class passengers can board in \(6!\) ways. This is calculated by using the factorial function: \(6! = 6 * 5 * 4 * 3 * 2 * 1\).
3Step 3: Calculate the total number of boarding order possibilities
The total number of boarding scenarios is the number of first-class boarding orders multiplied by the number of economy-class boarding orders: Total = \(2! * 6!\)
Other exercises in this chapter
Problem 17
In Exercises 9-32, write the first five terms of the sequence. (Assume that \( n \) begins with 1.) \( a_n = \dfrac{6n}{3n^2 - 1} \)
View solution Problem 18
In Exercises 15 - 20, find the probability for the experiment of tossing a coin three times. Use the sample space \( S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
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In Exercises 15 - 18, evaluate using Pascals Triangle. \( _10C_2 \)
View solution Problem 18
In Exercises 11 - 24, use mathematical induction to prove the formula for every positive integer \( n \). \( 1^3 + 2^3 + 3^3 + 4^3 + \cdots + n^3 = \dfrac{n^2\l
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