A space shuttle mission consists of a commander, a pilot, 3 engineers, a doctor, a scientist  and a civilian. If there are 7 people from whom the commander and the pilot must be chosen, 18 possible engineers, 4 doctors, 7 scientists and 3 civilian candidates for crew member, in how many ways can a crew be formed?

Q: There are 5 third year and 4 fourth year ECE students qualified to join a contest. In the group…

A: The number of ways to select r number of different objects from n number of different objects can be…

Q: president, a treasurer, and a secretary are to be chosen from a committee with forty members. In how…

A:

Q: A football squad consists of three centers, ten lineman who can play either guard or tackle, three…

A: Given: A football squad consists  3 center players, 10 lineman who can play either guard or tackle…

Q: In how many ways could a committee be formed that included 3 Conservatives, 3 Liberals, 2 NDP and 1…

A: Number of conservatives = 14 Number of Liberals = 23 Number of NDP = 8 Number of independent members…

Q: A bag contains 2 red marbles, 5 green ones, 1 lavender one, 5 yellows, and 3 orange marbles.  How…

A: Since we are making set, so the order will not matter.   If we select the lavender one, then we can…

Q: Out of 6 statistician and 8 mathematician, a special task force is to be formed consisting of 3…

A: A special task force is to be formed consisting of 3 statisticians and 4 mathematicians out of 6…

Q: In a club with 20 members, how many ways can a slate of 3 officers consisting of president,…

A: This question is related to permutation and combination. The solution is given below

Q: There are 20 seniors serving the student council of the Cebu Institute of Technology this year. Of…

A: Solution:  Given : n( Ω)=20 Let, A: 3 senior serving who not served before B : 10 serving in their…

Q: a. In how many ways can 3 civil engineers and 2 mechanical engineers be chosen from the applicants?…

A: Here use combination An Engineers Association has a couple of vacant positions and there are a total…

Q: A restaurant offers 4 different flavours of coffee, 3 different soup selections and 4 different…

A: From the provided information, A restaurant offers 4 different flavours of coffee, 3 different soup…

Q: A group of 11 people consisting of 1 freshmen, 3 sophomores, 3 juniors, and 4 seniors are selected…

A:

Q: A jury pool consists of 27 people. How many different ways can 11 people be chosen to serve on a…

A: 1. From the given information, a jury pool consists of 27 people.

Q: A baseball team has 5 left-handed and 12 right-handed hitters and 3 switch hitters (either left or…

A:

Q: Consider a bag containing four red marbles, three green ones, one transparent one, three yellow…

A: Given that there are 4 red marbles, 3 green ones, 1 transparent one, 3 yellow ones, and 2 orange…

Q: A class consists of 60 girls and 40 boys. In how many ways can a president, vice-president,…

A: Number of boys=40 Number of girls=60 Given the treasurer must be a girl. Hence the number of ways to…

Q: A clothing store has 13 shirts in 4 sizes: small, medium, large, and extra-large for sale. If it has…

A: Number of ways of selling two small shirts is 2! = 2 Number of ways of selling three medium shirts…

Q: From a student group of 70, 26 people play basketball, 36 people play football, 31 people play…

A: Union of Two Sets: For any two sets A and B, union of A and B, written as A∪B, contains the elements…

Q: club with eighteen members is to choose three​ officers: ​ president, vice-president, and​…

A: Topic:- permutation and combinations

Q: A club with nineteen members is to choose three​ officers: ​ president, vice-president, and​…

A: Permutation:   It is nothing but  an arrangement of objects with the definite order.   Let n is the…

Q: A certain congressional committee consists of 8 senators and 12 representatives. How many ways can a…

A: It is given the number of senators is 8 and representatives is 12.

Q: In a club with 8 members, how many ways can a slate of 3 officers consisting of president,…

A:

Q: Out of 5 class representatives and 7 prefects, a committee consisting of 2 class representatives and…

A:

Q: ee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores,…

A: The selection of elements without arrangement can be represented by a combination of elements. We…

Q: In a college football training session, the defensive coordinator needs to have 10 players standing…

A: Given information Total players = 10 1 freshmen 2 sophomore 4 juniors 3 Seniors

Q: ee has 9 members, consisting of 5 Republicans and 4 Democrats. An education group of 3 members is…

A: n= 9 R = 5 D = 4 Using the combination formula. Ways of selecting 3 members from 9 are:

Q: 59. Out of 5 mathematicians and 7 statisticians, a committee consisting of 2 mathematicians and 3…

A:

Q: In a cricket team there are 12 players, among these 12 players there is one captain, 4 batsmen, 3…

A: Given Information: In a cricket team there are 12 players, among these 12 players there is one…

Q: There are 8 women and 5 men signed up to join a swing dance class. In how many ways can the…

A:

Q: If 5 cards are dealt from a standard deck of​ cards, how many different ways can three spades and…

A: 5 cards are dealt from a standard deck of​ 52 cards. There are 13 spade cards. Therefore number of…

Q: Out of a group of 60 people, 20 invested in stock market, 35 had certificates of deposit, and 34 had…

A:

Q: Suppose a class consists of 3 students majoring in Islamic Studies, 4 students majoring in…

A:

Q: If a board has 5 women and 4 men. How many ways can you form a committee containing 3 members such…

A: Given that a board has 5 women and 4 men. Now we want to form a committee containing 3 members such…

Q: there are 6000 students at mountain high school and 3/4 of these students are seniors,if 2/3 of the…

A:

Q: The United States Senate Committee on Commerce, Science, and Transportation consists of 23 members,…

A: Combinations: The number of combinations of r items selected from n items is, nr=n!n-r!r! Selecting…

Q: A football squad consists of three centers, ten linemen who can play either guard or tackle, three…

A: Given A football squad consists of three centers, ten linemen who can play either guard or tackle,…

Q: Delegates from 10 countries, including Russia, France, England, and the United States, are to be…

A: Given  10 countries in total  4 of them are Russia, France, England, United States  We need to…

Q: A hockey team has five left wingers, four right wingers, three centres, four left defense, four…

A: To find: How many ways could the starting lineup be chosen?

Q: How many ways can a group of 7 blood donors be chosen from 5 type A donors, 5 type O donors, 4 type…

A:

Q: Suppose a class consists of 4 students majoring in Mathematics, 3 students majoring in Computer…

A: Number of students in mathematics MS= 4 Number of students in computer science CS = 3 Number of…

Q: A co-rec team to play in an intramural tournament of indoor soccer should consist of three men and…

A: Let us suppose there are three marbles viz. a red, a green and a blue. From these, there are three…

Q: A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated…

A:

Q: how many ways can 2 men, 3 women, 4 boys, and 5 girls be selected from 4 men, 5 women, 6 boys and 7…

A:

Q: a club consists of 5 men and 4 women. in how many ways can this club elect a president, Vice…

A: Given data A club consists of 5 men and 4 women

Q: A group of 13 people consisting of 3 freshmen, 2 sophomores, 4 juniors, and 4 seniors are selected…

A: Given: A group of 13 people is to be formed by selecting, 3 freshmen out of 6 freshmen, 2 sophomores…

Q: A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are selected…

A: Given:A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are…

Q: A research team of 7 members must be formed from a group of 10 teachers consisting of 3 senior…

A: Given: Total members (n)=10number of seniors (s)=3number of juniors (j)=4number of rookie(r)=3Number…

Q: In a group of 7 professional courses and 6 math courses, 3 courses are to be selected. Give option 3…

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Q: A company has 7 male and 12 female employees, and needs to nominate 2 men and 2 women for the…

A:

Q: There are  10  women and  5  men signed up to join a ballroom dance class. In how many ways can…

A:

Q: A restaurant offers a 4 kinds of soup, 7 kinds of main dish, 5 kinds of vegetable dish, and 6 kinds…

A: A restaurant offers a 4 kinds of soup, 7 kinds of main dish, 5 kinds of vegetable dish, and 6 kinds…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.