QUESTION 12. The combination of 11 things taken 8 at a time ( 11 C 8) is exactly the same as 11 things taken 3 at a time (11 C 3). Explain why this is logical and not just a coincidence.

Q: A group of four students studying for a bar exam has formed a study group. Each member of the group…

A:

Q: A manager wants to award prizes for 1", 2nd and 3rd to his team members according to number of new…

A: We have given that the team is formed of 25 members and the prizes be awarded.    Permutation…

Q: 1 red, 1 blue, 1 black, 1 yellow and 1 white car are all waiting at the traffic lights behind each…

A:

Q: In how many ways can a student answer 5 out of 8 questions if he is required to answer 3 of the…

A: Here use combination

Q: In how many ways can a commitee of 9 students be chosen from 8 juniors and 10 seniors if there must…

A: Given data: 8 juniors and 10 seniors

Q: In how many ways can one put 8 adults and 4 children in a row, such that no two children are next to…

A: We have given that there are 8 adults and 4 children in a row. Here our claim to to show in how many…

Q: In a class, there are 6 boys and 5 girls. How many ways can we form a committee / group / team of 6…

A: The number of boys and girls in the class are 6 and 5 respectively. The committee must be formed…

Q: In how many ways can three awards be given to seven students under the following conditions :  If…

A: If student can receive more than one award. There are three rewards. Each reward can be assigned to…

Q: Your school locker has a dial with 50 numbers which required 3 numbers to open. (It is not a…

A: We have to find out given n...

Q: Suppose there is a list of six jokes about marriage and divorce. In how many ways can people select…

A: The objective of this question is to find out the number of ways people can select their two…

Q: Jeremiah has six boxes of six different sizes. Four boxes are taken at a time and arranged in…

A: Given that, Jeremiah has six boxes of six different sizes. Four boxes are taken at a time and…

Q: In how many ways can a team of 11 players be chosen from 14 players if the captain and his assistant…

A: This is problem of counting and we will solve this using combination.

Q: If there is 1 person in a room and no one shakes his or her hand, and then someone else enters the…

A: Let n be the number of persons in the room.

Q: n how many ways can 5 men, 4 women, and 3 children be arranged in a row of 12 seats if a. the men…

A: Given that  Number of men = 5 Number of women = 4 Number of children = 3 Number of seats in the row…

Q: In how many ways can 3 mathematics books, 5 science books, and 2 language books be arranged in a…

A:

Q: If 2 specific persons among the 10 people lined up to get on the bus refuse on following each other…

A:

Q: Three cards are chosen without replacement from a deck of 52 cards and placed in order from first to…

A: In the deck of 52 cards, there are total 4 6's. (One for each of hearts, diamonds, spades and clubs)…

Q: Assume that the committee consists of 11 members including Julie. The same three offices are to be…

A:

Q: A mother, father, and their three children are to line up for a photo. In how many ways can these…

A:

Q: how many ways can 5 textbooks, 3 coffee table books and 2 novels be arranged if the textbooks must…

A: This question is from permutation We have to calculate, in how many ways 5 textbooks, 3 coffee table…

Q: In one state, each automobile license plate shows three letters followed by two digits, or two…

A: The number of letters in alphabet is 26. The number of digits from 0 to 9 is 10.

Q: Example 26. In how many ways can 7 gentlemen and 7 ladies be seated at a round table so that no 2…

A:

Q: How many different words consisting of 13 letters can be written such that exactly 4 of the letters…

A: Total Letter=13=4(A)+4(B)+5(C) Then number ways = ?

Q: I am the smallest number expressed in ones, tens, hundreds, and thousands. All my digits are less…

A: Let's consider each condition one by one- All of the four digits are less than seven, so the numbers…

Q: 2. Every 2nd and 4th Thursday this semester around 2:30 you see your teacher go to room A101. You…

A: Solution ) inductive reasoning )  in this type of reasoning we take some observation  and based on…

Q: In how many ways can we seat 6 boys and 3 girls on a row of seats so that no two girls sit next to…

A: If no two girls can sit together, then we need to alternate boy and girl. We can start with a boy…

Q: Assume that the committee consists of 13 members including Bill. The same three offices are to be…

A: Given, Assume that the committee consists of 13 members including Bill. The same three offices are…

Q: In how many ways can you arrange 6 distinct maths books and 5 distinct physics books on a shelf, if…

A:

Q: Show your work and justify. In how many ways can we order a deck of 52 playing cards so that no two…

A:

Q: You want to arrange the letters of the word ”MISSISSIPPI” such that all the ’I’s come together. How…

A: MISSISSIPPI

Q: In how many ways can four English books, three statistics books, three chemistry books and two…

A: Number of English books = 4 Number of statistics book = 3 Number of chemistry book = 3 Number of…

Q: How many three-letter "words" (some may be nonsense words) can be made from 4 letters "FGHI" if…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: In how many ways can 3 English, 3 history, and 3 math books be set on a shelf, if the English books…

A:

Q: 3n couples and their one child sit at a round table in such a way that their one child is between a…

A: It is given that there are 3n couples and their one child sit at a round table in such a way that…

Q: How many ways are there of arranging the 26 letters of the alphabet so that none of the words be,…

A:

Q: A group of five students studying for a bar exam has formed a study group. Each member of the group…

A: Permutation:   A permutation is an arrangement of objects in a definite order.   Let n is the total…

Q: John was born on February 28, 1999. It was a Sunday. February of that year had only 28 days, and the…

A: John’s birthday on 28 February 1999. Jacks birthday on 29 the February 2000. The total number of…

Q: There are possible different routes. (Simplify your answer.)

A: n = 7 r = 5

Q: A true-false quiz contains 15 questions. In how many ways can a student answer the questions if the…

A: A true-false quiz contains 15 questions. The number of ways such that student answer 7 false…