Answered: If a theatre holds 1300 people, how…

If a theatre holds 1300 people, how many seats need to filled to ensure that two people have the same first and last initial? Use PigeonHole Principle to solve.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: A high school student needs 9 more classes to graduate. If she has met the prerequisites for all…

A: Given information Students need 9 more classes to graduate No of class periods to fill = 5

Q: A tank originally contains 100 gal of fresh water. Then water containing - lb of salt per gallon is…

Q: A bathroom tub will fill in 15 minutes with both faucets open and the stopper in place. With both…

A: To Determine: How long will it take for the tub to fill if both faucets are open and the stopper is…

Q: One-North Warehousing Services block stacks its SKUs in 50 rows. Each row is 3 deep and stack 3…

A: The number of items in a stack can be calculated by multiplying the number of rows by the number of…

Q: Determine the average total time in the system

A: Given that the service rate is μ = 50 customers per minute and the average number of customers in…

Q: The service elevator at AR Hector Financial Complex has a maximum capacity of 2870 lbs. If the…

A: Given: The service elevator at AR Hector Financial Complex has a maximum capacity of 2870 lbs. The…

Q: The Ritz Hotel has enough space for six taxicabs to loadpassengers, line up, and wait for guests at…

A: a) Here, λ=1/10 μ = 1/3.5 ρ = λ/ μ =3.5/10 =0.35 The average waiting time is calculated as follows:…

Q: A farmer would like to evaluate Miracle Grow when used on his potted daisy plants. He sets up 20…

A: Step 1: Since you have posted a question with multiple sub parts we will solve the first three parts…

Q: An instructor has graded 30 exam papers submitted by students in a class of 31 students, and the…

A: Answer Given 30 exam papers31 studentsaverage =68

Q: At the beginning of year 1, the population of the country of Freedonia has 3450 people. Each year,…

A: Given at the beginning of year 1, the population of the country of Freedonia has 3450 people. Each…

Q: You were project manager of 5 identical projects and needs to designate workers for 5 identical…

A: Given problem:- You were project manager of 5 identical projects and needs to designate workers for…

Q: Females of American crocodiles (Crocodylus acutus) produce on average 50 eggs. Consider one…

A: From the given information, the females of American crocodiles produce on average of 50 eggs. The…

Q: Initially, there are 400 bacteria and after 9 hours, 900 bacteria are observed in the culture. Find…

Q: Suppose that 5 bulldozers can load 8 trucks full of gravel in 40 minutes. Assume all bull dozers…

A: Consider the given: 5 bulldozers can load = 8 trucks1 bulldozer can load = 85 trucks4 bulldozer…

Q: There is a factory that makes widgets in different colors. The production time for each color is…

A: Given: Here are the given story's summary, The factory in question makes widgets in two colors -…

Q: CCL is a container shipping company that provides ocean transportation services between hong kong…

A: The round-trip transit time for this route, including the stoppage time at multiple ports along the…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 5 health inspectors test two batches of vaccines of 30 doses…

A: We have 5 health inspectors. First batch has 30 doses and second batch has 30 doses. Each inspector…

Q: 3) When members of the military are in a combat zone, they often eat meals-ready- to-eat (MRES). A…

A: First, determine the calories consumed in one day. Now convert the other units into days. Now use…

Q: If ten components are to be stacked into a cylindrical casing. Component 1 and 2 need to be at the…

A: Given three components are of one type and identical to one another and two components areof…

Q: An instructor has graded 23 exam papers submitted by students in a class of 24 students, and the…

A: Given An instructor has graded 23 exam papers submitted by students in a class of 24 students, and…

Q: A small metal bar with initial temperature was 20°C, is dropped into a large container of water with…

A: Here we create a differential equation based on given information. Then solve that equation.

Q: At a factory, 2,500 pairs of jeans is needed to be produced in 60 days. 12 tailors had already…

A: The tailor needed to complete remaining work in remaining days =7

Q: The Escherichia coli culture (better known as E. coli) doubles every 40 minutes. If 30 E. coli are…

Q: Initially, there are 400 bacteria and after 9 hours, 900 bacteria are observed in the culture. Find…

Q: A research study in a big metropolitan area shows that 2% of individuals living within the city…

A: Given information: It is given that, 2% of the individuals living within the city limits move to…

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

If a theatre holds 1300 people, how many seats need to filled to ensure that two people have the same first and last initial?

Use PigeonHole Principle to solve.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

A and B can do a piece of work in 12 days; B and C can do it in 15 days while C and A can finish it in 20 days. In how many days will A,B,C finish it, working togeteher? In hpw many days will each one of them finish it, working alone?
Two persons are to run a race, but one can run 9 meters per second, whereas the other can run 5 meters per second. If the slower runner has a 50-meter head start, how long will it before the faster runner catches the slower runner, if they begin at the same time?
The workers of the company "Malova" work in a 5-day work week and worked them for 22 days in the month of November 2020. The standard work schedule is 8 hours per day with a 30-minute break included in this time. Now, "Malova's" company is in the process of manufacturing screwdrivers and manufactured 3100 pieces of screwdrivers. In addition, the company manufactures screwdrivers in batches of 300 and after each batch makes a pause to check the quality of production and make certain adjustments to the machines if necessary. The break is 1 hour. Calculate the parts produced per hour by the Malova company in November. Important: Use the formula (the one I put in the image)
11 A rope of length 205 m is cut into 10 pieces of one length and 5 pieces of another length. The total kength of three of the fint 10 lengths exceeds that of two the second length by 2 m. Find the lengths of the picces.
Arrange these steps in the correct order to prove that if you have an 8-gallon jug of water and two empty jugs with capacities of 5 gallons and 3 gallons, respectively, then you can measure 4 gallons by successively pouring some of or all of the water in a jug into another jug in the correct order. Rank the options below. Fill the 3-gallon jug from the 5-gallon jug, leaving (3, 2, 3). Empty the 5-gallon jug's contents into the 3-gallon jug, leaving (6, 0, 2), and then fill the 5-gallon jug from the 8-gallon jug, producing (1, 5, 2). Fill the 5-gallon jug from the 8-gallon jug, leaving the contents (3, 5, 0), where the ordered triple is used to record the amount of water in the 8-gallon jug, the 5-gallon jug, and the 3-gallon jug, respectively. Top off the 3-gallon jug from the 5-gallon jug, and there will be (1, 4, 3), with four gallons in the 5-gallon jug. Pour the contents of the 3-gallon jug back into the 8-gallon jug, leaving (6, 2, 0). ❤ ← ←
A worker uses 560 inches of steel wire to make 350 springs of the same size. At training rate, how many inches of steel wire are needed to make 1 spring?