Using permutations and combonations:  A croissant shop has 7 types of croissants: plain, cherry, chocolate, almond, apple, cheese and hazelnut croissants. How many ways are there to choose: a) one dozen croissants? b) one dozen croissants with at least one of each kind? c) one dozen croissants with 2 plain, 1 cherry and at least 2 chocolate?

Q: How many six-person volleyball teams be made from a group of six men and three women if: a. If two…

A:

Q: 2. In a group of 45 students, 23 take history, 18 take biology and 10 take both history and biology.…

A: Given :  Total number of students = 45 Number of students taking history = 23 Number of students…

Q: There are five pictures but only four display cases. The display cases are unique. How many…

A: The number of pictures is 5. The number of display cases is 4. The display cases are unique.

Q: Suppose you are ordering a calzone from D.P. Dough. You want 6 distinct toppings, chosen from their…

A: Since we want 6 distinct toppings chosen from a list of 8 vegetarian toppings, this is a combination…

Q: There are 10 students in a class. In how many ways can an instructor give at most three students a…

A: n = 10 Let x represent the number of students given grade A.   The number of ways a student can be…

Q: In a school of 200 students, a math team, consisting of 15 students, is to be formed. Two team…

A:

Q: 3. At Wingstop, customers ordering a family meal can choose 4 different wing flavors. If Wingstop…

A: Answer - At Wingstop,  customers ordering a family meal can choose 4 different wing flavors.…

Q: filaterals can you draw using the dots below as verti quadrilaterals possible in the previous…

A: *Answer:

Q: A student has 20 video games: 4 adventure games, 6 arcade games, 5 puzzle games, and 5 simulation…

A: Given : A student has 20 video games : 4 adventure games , 6 arcade games , 5 puzzle games and 5…

Q: 5) An ice cream shop has 10 flavours of ice cream and 7 toppings. Their megasundae consists of your…

A:

Q: a. moblle phone snop has plors of 0, 8 of headphone. In how many ways a customer can che with a…

A: Given, A mobile shop has : 7 colors of ipad 8 colors of HCT mobile 4 colors of headphone     to find…

Q: A mobile phone shop has 7 colors of iPad, 8 colors of HCT mobile phones and four colors of…

A:

Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1<x2 then fx1>fx2 claim- is it decreasing or increasing

Q: Count.... a) 18 5 b. How many different 5-person teams can be formed from 15 students?

A: a) 8568 b) 3003

Q: Ahmad, Ben and Charlie had 189 pencils altogether. After Ahmad gave 3/10 of his pencils to Ben and…

A: Ahmad, Ben and Charlie had 189 pencils altogether. After Ahmad gave 3/10 of his pencils to Ben and…

Q: Suppose you are ordering a calzone from D.P. Dough. You want 6 distinct toppings, chosen from their…

A:

Q: A coffee shop offers five different flavors of coffee and three flavors of doughnuts. How many…

A:

Q: When ordering a certain type of computer, there are four choices of hard drive, three choices for…

A: Number of choices for hard drive = 4Number of choices for memory = 3Number of choices for video card…

Q: A baseball team has 14 players. How many 9​-player batting orders are​ possible?

A: Given : A baseball team has 14 players.

Q: Maria needs to take three physical education classes in order to graduate. Her college has 12…

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: After the tryouts for the volleyball team, the coach selects 14 people to join the team. Due to a…

A: To determine the number of ways the coach can choose 7 people out of 14, we use the combinations…

Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

A:

Q: An order of lumber has 36 boards 12 ft long, 28 boards 10 ft long, 36 boards 8 ft long, and 12…

A:

Q: Written Respons 1) A school's debate team consists of 9 students and must consist of at most 3 boys.…

A: Given- A school's debate team consists of 9 students. 12 boys and 9 girls try out for the team. The…

Q: Assume that a grade of A, B, C, D, F, or NC is assigned to each of 10 students. In how many…

A: Given ,Grades are  A, B,C,D,F or NCTotal grades = 6No. of students = 10

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.