**Problem Statement:**In a mathematical competition, there were twenty-one girls and twenty-one boys. It was found that:(a) Each contestant solved at most six problems.(b) For each pair of a girl and a boy, there was at least one problem that both of them solved.**Objective:**Prove that there is a problem that was solved by at least three girls and at least three boys.**Explanation:**To solve this problem, it's crucial to analyze the conditions given and understand the constraints. The goal is to demonstrate the existence of a particular problem that is commonly solved by a minimum of three girls and three boys, adhering to the competition rules. This involves logical reasoning and potentially using techniques from combinatorics or graph theory.

Given Information: Number of girls in a mathematical competition is 21 Number of boys in a…

Answered: I'wenty-one girls and twenty-one boys…

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

Similar questions

A minor league baseball team had 7000 fans in attendance, and total ticket receipts were $26,400. Box seats cost $6, grandstand seats cost $4, and bleacher seats cost $2. If the number of tickets sold for box seats was one-third the number of bleacher seats sold, how many tickets of each type were sold? Lial, Margaret L.. Finite Mathematics with Applications In the Management, Natural, and Social Sciences (p. 293). Pearson Education. Kindle Edition.
Use the formula for „P, to solve the following question. A club with nine members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled? ways
Decide whether the exercise involves permutations or combinations, and then solve the problem. In a club with 11 male and 10 female members, how many 5-member committees can be chosen that have (a) at least 4 women? (b) no more than 2 men? Does the problem involve permutations or combinations? (a) There can be nothing 5-member committees with at least 4 women.
An event planner is deciding what food to include in a buffet. The caterer has offered 10 cold dishes and 6 hot dishes. Of the 16 dishes offered, the event planner will choose 8. (If necessary, consult a list of formulas.) (a) In how many ways can the event planner choose 8 dishes if the number of hot dishes must be less than 2? 0 (b) In how many ways can the event planner choose 8 dishes if the number of hot dishes must be greater than or equal to 2? 0 Explanation Check O M X S F 10 Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center Accessi
A student in a statistics class is going to select 5 of her classmates to ask a survey question. Of her 19 classmates, there are 8 students who live on campus and 11 students who live off campus. (a) In how many ways can she select 5 classmates if the number of students who live off campus must be greater than 2? (b) In how many ways can she select 5 classmates if the number of students who live off campus must be less than or equal to 2?
Jack packs 3 pairs of shoes, 4 pairs of boots, 8 pairs of jeans, 9 pairs of dress pants, and 2 dress shirts for a trip. (a) How many different outfits can Jack make with these items? (b) If Jack were to bring along 4 sweaters so that he could wear either a dress shirt or a sweater or he could wear both a dress shirt and a sweater, how many outfits could Jack make? (a) Jack can make (Type a whole number.) different outfits with these items. (b) Jack can make different outfits with these items. (Type a whole number.)
Please don't provide handwritten solution ...
Help me fast so that I will give good rating.
Maa
(a) In how many ways can 4 boys and 3 girls sit in a row. (b) In how many ways can they sit in a row if the boys and girls dare each to sit together
A bagel shop has a selection of 8 different kinds of bagels (at least 10 of each). (.1) How many different selections of 10 bagels can be made? ( .2) If garlic is one kind of available bagel and onion is another, how many different selections of 10 bagels can you make so that you have at least 3 onion bagels and exactly 2 garlic bagels?
Mrs. Smith has 6 activity tables she wants to line up side by side in her classroom. (a) In how many ways can she arrange all 6 tables? Show your work.(b) If she only wants to have 4 of the tables set up, in how many ways can she choose the tables shewishes to have set up? Show your work. Answer:

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS