A deli offers 6 different toppings. You are allowed 4 different toppings. In other words, you can't select the same topping more than one more time per sandwich. How many choices of 4 toppings are th

Q: how many four digit numbers can be formed if all the digits are odd numbers and each digit can be…

A: Using the 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, here 4 digit numbers are formed in which all…

Q: instructors will be chosen from 20 applicants to do a Ph.D program within their field with a…

A: To find group ,it is combination and to find arrangements it is permutations.

Q: 2. How many ways can 10 books be arranged in a shelf if one of them is a bible and it must be placed…

A: Given that, 2.  10 books be arranged in a shelf & one of them is a bible and it must be placed…

Q: 3. Suppose 1500 runners are in a race. How many ways could the runners finish in 1t, 2nd and 3rd…

A:

Q: Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to…

A: Three married couples are to be seated in a row having six seats in a cinema hall. We have three…

Q: Assune that you have a committee of 12 members, made up of 3 men and 9 women. In how many ways can…

A: Given, 12 members in the committee, made up 3 men and 9 women  To find the number of ways 3 tasks be…

Q: How many 5 letter "words" can be formed if exactly 2 of the letters are vowels?  Condition: order is…

A: Let there are three persons A, B and C sitting beside each other. The different ways in which this…

Q: HOW MANY WAYS 4 PIZZA TOPPINGS BE SELECTED FROM A CHOICE OF 12 TOPPINGS CAN BE CHOSEN ONLY ONCE?

A:

Q: How many 3-digit number greater than 200 can be formed (a) repetition not allowed (b) repetition…

A:

Q: If order of items is important when selecting some of n unique items, the number of arrangements are…

A: By order being important, we mean that (a, b) and (b, a) are not equal. For example, if we are…

Q: Compute the number of ways we can select n fruits from 4 types of fruit (assume an unlimited supply…

A: Given 4 types of fruit (apple, banana, orange and peach)

Q: In how many ways can you distribute n pennies to k children if each child is supposed to get at…

A:

Q: . Bricks are stacked in 20 rows such that each row has a fixed number of bricks more than the row…

A:

Q: A man has time to play roulette 5 times. He wins or loses $ 1000 in every game. The man starts with…

A: Given information: Wins or loses per game = $1000

Q: A company has 10 different warehouses for storing their inventory. They will be storing 100…

A: Given:-             A company has 10 different warehouses for storing their inventory. They will be…

Q: How many combinations are possible? Assume the items are distinct. 9 items chosen 6 at a time…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

Q: How many combinations are possible? Assume the items are distinct. 5 items chosen 3 at a time…

A:

Q: A lottery game requires that 6 different numbers are picked from 1 to 11. If someone picks all 6…

A:

Q: A large amphitheater is set up in such a way that there are 16 seats in the first row 27 seats in…

A: The given problem is regarding arithmetic progression series. First-term is given. A common…

Q: A license plate in a certain county consists of 4 letters followed by 3 single digits.  How many…

A: Permutation is deals with arrangements. It is used to calculate the number of ways a certain number…

Q: In how many different way can a person choose 2 desserts from a menu of 12

A:

Q: #4. There are five rooms to be given to five students clubs for their meeting rooms. Find the total…

A: The number of ways r items can be selected from n items is, nr=n!r! n-r! There are 5 rooms to be…

Q: You are ordering an extra large pizza with multiple toppings on it. In how many ways can 6 different…

A:

Q: How

A:

Q: One hundred candy bars are to distributed one at a time among 4 children. If no child can receive…

A: Normal 0 false false false EN-IN X-NONE X-NONE…

Q: Compute the number of ways we can select n fruits from 4 types of fruit (assume an unlimited supply…

A: Given Number of apples is even Number of bananas is a multiple of 5 Find The number of ways we can…

Q: How many ways that 2 girls and 4 boys can fall in a line of there must be a girl and a boy in the…

A:

Q: how many five letter codes can be made if each chosen letter (from the the original 7 letters) can…

A:

Q: How many plates are possible each plate consists of three letters followed by three digits excluding…

A:

Q: How many strings of 7 English letters are there that start and end with the letter T and contain at…

A: Given, we have to make 7 letters string that  will start and end with T    And the string have at…

Q: How many different meals are possible from a menu if you choose one each of 5 appetizers, 4 entrées,…

A:

Q: How many combinations are possible? assume the Items are distinct. 5 items chosen 2 at a time

A: C(n,r) = n! /{r! (n-r)!}

Q: From 8 candidates if 3 are selected for Open Scholarships. How many possible options are available…

A:

Q: candidate receives 62% of the vote in an election and there are 1603 votes recorded. What is a…

A:

Q: Suppose we select 3 students randomly out of a class of 10 students to read a paper from the…

A:

Q: erfect pizza has 15 toppings listed on their menu. How many ways could a customer choose pizza that…

A:

Q: A group consists of 6 men and 5 women. Four people are selected to attend a conference. In how many…

A: We have to solve above question and find probability

Q: A committee of 3 is to be formed from a group of 20 people. How many different committee are…

A: A committee of 3 is to be formed from 20 people. So there has to be 3 selections from 20 people…

Q: What if the jelly bean machine gives 9 jelly beans to the first customer who put in a coin, 13 to…

A: For an arithmetic sequence, the difference between the consecutive terms is a constant. The nth term…

Q: A basket of fruit is being assembled from apples, bananas, and oranges. What is the fewest number of…

A: Given question is A basket of fruit is being assembled from apples, bananas, and oranges. What is…

Q: In how many ways can 2 pizza toppings be chosen from 12 available topping Your answer is :

A: Given : n = 12  r = 2

Q: itially, 10 people have an infection. The next day, every infected people infects one more person.…

A: To find the number of days it will take for 1280 people to infect.

Q: A license plate is a sequence of 2 letters followed by 2 different digits.     A letter is A…

A: There are totally 26 letter and 10 digits. A license plate is a sequence of 2 letters followed by 2…

Q: in a rugby match, a tie at the end of two overtime. Leads to a shoot out with five cakes taken by…

A: GivenLeads to a shoot out with five cakes taken by each team from the center of the 22 m line. Each…

Q: A sheet of paper is cut into 2 same size parts. Each of the parts is then cut into 2 same- size…

A: Let's figure out how it goes with the number of cuts: Number of cuts pieces of paper…

Q: How many different arrangements of 4 letters can be formed if the first letter must be W or K…

A: Total no.of letters(A to Z)=26

Q: A grocery store sells 10 different types of sodas sold in six-packs with at least 200 of each type…

A: We know that if we have to choose r items out of n items with repetition allowed, number of such…

Q: Red and blue ceramic tiles are laid according to a pattern such that for every 22 red tiles used, 3…

A: Given that there are total 300 ties of Red and blue colour .according to pattern every 22 red…

Q: A five-person committee is to be selected from an organization's membership of 19 people. How many…

A: It is given that, An organization has 19 people out of which 5 person committee is to be selected.…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.