How many poles will there be in a stack of telephone poles if there are 58 in the first layer, 57 in the second, 56 in the third, and so on, with 12 in the top layer?

Q: How many possible meals are there?

A: here use fundamental of counting principle   The school canteen offers the following choices for…

Q: How many three-digit numbers can be formed of the digits 1, 2, 3, 4, 5, and 6 if each digit can only…

A: There are 6 numbers. The required three digit numbers can be formed using the numbers 1, 2, 3, 4, 5,…

Q: How many different teams of 44 can be chosen from a group of 1818 children and 1515 adults if each…

A: It is given that the number of children is 18 and the number of adults is 15.

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

A:

Q: How many numbers can be formed from the digits 1, 2, 3, and 4 if repetitions are not allowed?

A: How many numbers can be formed from the digits 1, 2, 3, and 4 if repetitions are not allowed.

Q: Suppose 84% of students chose to study Spanish their junior year, and that meant that there were 378…

A: Then,

Q: If a person can select five books from a list of ten, how many different combinations are there?

A: Given data: The total numbers of books are n=10. The number of books selected is r=5. The expression…

Q: In how many ways can an advertising agency promote 12 items 6 at a time during a 12 - minute period…

A: Given that, n= 12 And = 6

Q: In how many ways can six books be lined up along a shelf?

A:

Q: Telephone poles are being stored in a pile with  25 poles in the first layer, 24 in the second, and…

A: Explanation: According to the question:  In a pile,  1st layer contains = 25 poles 2nd layer…

Q: Suppose the Department of Motor Vehicles uses six digits and the numbers 0 through 9 to create its…

A: Solution.

Q: Assume that the candle manufacturer has 7 types of round candles and 5 types of square candles…

A: Permutations and combinations: When one has to choose among a set of objects or people, then…

Q: How many ways can 120 unique packages be loaded into 10 delivery trucks where each truck must have…

A: 120 distinct packages have to be distributed equally among the 10 trucks.

Q: At a music​ festival, there are ten bands scheduled to​ play, numbered 1 through 10. a. How many…

A: At a music​ festival, there are ten bands scheduled to​ play, numbered 1 through 10.   a. Number of…

Q: How many​ 10-digit telephone numbers​ (area code+​number) are possible if the first digit cannot be​…

A:

Q: Telephone poles are being stored in a pile with 25 poles in the first layer, 24 in the second 23 in…

A: Given that Telephone poles are being stored in a pile with 25 poles in the first layer, 24 in the…

Q: Five of ten books are arranged on a shelf. In how Many waYS Can this be done?

A:

Q: How many ways are there to select 9 countries in the United Nations to serve on a council,if 3 are…

A: This question is related to permutations and combinations, we will solve it using given information.…

Q: A credit card company gives each of its customers a 4-digit PIN where each digit is selected from…

A: Multiplication rule of counting:If a task consists of a sequence of choices in which there are ‘a’…

Q: If 162 strings of lights were disposed of last week because they were deficient, how many strings of…

A:

Q: How many 3-letter passwords can be made using the letters A through Z if... a) Repetition of…

A: We have to find the number of 3-letter passwords that can be made using the letters A through Z if…

Q: In an examination, 80 candidates offered Mathematics, 90 candidates offered English and 55…

A:

Q: 1. How many different committees of 3 chemists and 2 physicist can be formed from the 8 chemists and…

A:

Q: For a group of 9 representatives, how many committees of size 3 are possible without any…

A:

Q: How many different committees of size  3  can be formed from  15  people?

A:

Q: a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit…

A:

Q: How many different patchwork quilts, four patches long and three patches wide, can be made from five…

A: Given: Five red and seven blue squares.   To determine: The number of different patchwork quilts…

Q: A state makes license plates with two letters followed by four numbers. if no repetitions of the…

A: The license plates must consist of two letters followed by four numbers.

Q: How many three-digit numbers can be formed from the digits 1, 2, 3, 5, and 6, if each digit can be…

A:

Q: Certain automobile license plates consist of a sequence of three letters followed by four digits. If…

A: We have a license plate that consists of a sequence of three letters followed by four digits. The…

Q: Ten people split up into five groups of two each.  In how many ways can this be done?

A: The number of combinations of r items from a group of n items where the order is not important is…

Q: A large pile of coins consists of pennies, nickels, dimes, and quarters (at least 20 of each). How…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: How many seven-digit numbers can be made from the digits 1 to 9 if repetition is allowed?

A: Given that  To find the number of ways of 7 digit number can be made from the 1 to 9

Q: A company buys 9 computers, and it plans to connect each pair of computers by a cable (one cable per…

A: Given that there are total 9 computers. They will connect each pair of computers. That means we have…

Q: how many ordered lists are there of three items chosen from six ?

A:

Q: In a certain state, all car license plates have four capital letters followed by three digits. How…

A: Given Car license plates have 4 (A to Z) capital letters followed by 3 (0 to 9) digits

Q: How many 5-digit license plate numbers can we generate from the numbers, 0, 1, 2, 3, and 4 if it…

A: Given: There are 5digits 0 , 1 , 2 , 3 , 4 We need to count number of  5 digit number plates…

Q: A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes…

A: Here , particular brand of shirt comes in 12 colors. It has female version and male version. And it…

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

Q: Suppose that we have 10 numbered blocks, 2 RED, 3 BLUE, 4 GREEN, and one WHITE.  How many ways can…

A:

Q: How many elements are in the set {0, {0}}?

A:

Q: In a certain company 80 of the employees are men. What is the total number of employees if 5 out of…

A: given In a certain company 80 of the employees are men. To Determine the total number of employees…

Q: how many ways can the books be arranged on a shelf if books of the same subject must be placed…

A: here given  there are total 4 different mathematics books and 5 different science book here use…

Q: A license plate consists of two letters and three digits. How many different plates can be made if…

A: no.of digits (0 to 9)=10no.of letters (A to Z)=26

Q: Can you do this problem?

A: Given:Number of paintings are (n) = 9.Number of paintings selected to hang side by side in a gallery…

Q: Out of a population of 52 people, how many possible samples of size 2 are there?

A: Given information- Population size, n = 52 Sample size = 2 We have to find the number of possible…

Q: How many license plates are possible if they consist of 1 digit followed by 1 letter followed by 5…

A:

Q: How many ways are there to select 12 countries in the United Nations to serve on a council if 2 are…

A:

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

A: There are 5 vowels and 21 consonants. Here, the order is important.

Q: How many four-digit numbers can be made from the digits 1 to 6 if repetition is allowed?

A: Number of four digit can be made from digits  1 to 6 :

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.