An awards dinner is being planned by an organization. Answer the following questions concerning its preparation: There are 27 members in the organization and each member may bring two guests. How many may be in attendance if there is also a guest speaker? a.

Q: A volleyball team will be dispatched from a school. If the current volleyball club has 10 members,…

A: A volleyball team has 6 members . Here, there are 10 members in club and we need only 6 of them.

Q: there are 6 men and 7 women in the math club. a committee is to be formed consisting of 3 men and 4…

A:

Q: There are 32 teams attending the World Football Cup in Qatar. How many ways the championship team,…

A:

Q: Five people applied for jobs at a store. Only two of these people will be hired. The number of…

A:

Q: There are 13 members on a board of directors. If they must form a subcommittee of 6 ​members, how…

A: The objective of this question is to find out the number of different subcommittees that can be…

Q: There are 79 people protesting the destruction of the rain forests. There are 31 ​males, 24 of whom…

A:

Q: A store sells 8 kinds of balloons with at least 30 of each kind. How many different combinations of…

A: 8 kinds of balloons with at least 30 of each kind We have to find how many different combinations of…

Q: There are 18 males and 14 females in a classroom. A president, secretary and vice- president must be…

A: There are 18 males and 14 females in a classroom. A president, secretary and vice president must be…

Q: There are 4 purple plates and 4 blue plates? How many different ways can the plates be stacked? Two…

A: see the hand written solution:

Q: A company has 42 employees. How many different ways can 7 people be chosen to serve on a committee…

A: We can choose the 7 persons in 42C7 ways  Where 7 people are chosen then there are (42-7)=35 people…

Q: There are 29 students in a homeroom. How many different ways can they be chosen to be elected…

A: Given,Total no.of students=29

Q: A dish contains 2 yellow, 4 red, 5 purple, 2 green, and 3 orange candies.  How many sets of 6…

A: A dish contains 2 yellow, 4 red, 5 purple, 2 green, and 3 orange candies.

Q: The organizer of a conference is selecting workshops to include. She will select from 9 workshops…

A: Here we have to use concept of combinations.

Q: A club with 23 members must choose a president, a vice president, a treasurer, and a secretary. How…

A: n=23r=4

Q: lon.)

A: Given: Total number of players in a team are 16.            Number of positions are 9. To find:…

Q: A clown owns 8 hat(s), 7 horn(s), 6 oufits. How many different outfits can the clown put together if…

A: Solution

Q: A box has 15 pens in it, a class buys 5 boxes, how many pens are are in all boxes?

A:

Q: A state has license plates that consist of 2 letters followed by 3 numbers and each letter and…

A:

Q: A four-person committee is to be selected from an organization’s membership of 12 people.  How many…

A:

Q: Radio stations that are on the eastside of a nation have call letters consisting of a W followed by…

A: Here we have to number of five letter call letters starting from W

Q: A class has 13 ​students, of which 4 are seniors. How many committees of size 4 can be selected if…

A: Combination of n objects taken r at a time = n!(n-r)!r! where 0≤r≤n.

Q: In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the…

A:

Q: A dish contains 2 yellow, 4 red, 5 purple, 2 green, and 3 orange candies.  How many sets of 7…

A:

Q: A student must take 4 electives from a set of 10 electives. How many ways can the student choose the…

A: Solution-: Given: n=10, r=4 We want to find how many ways can the student choose the electives.

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.