What is the smallest number that can be represented as the sum of four positive squares (not necessarily unique) in two different ways?

Q: How many ways can a 4 member committee be selected from a club with 15 members? If the club's 15…

A: Given that there are 15 members. In 15 members, 8 are men and 7 are women.

Q: Tony and Maria are two star-crossed lovers trying to get on a committee of 4 people. If there are 10…

A: Consider that the 10 people includes Tony and Maria.

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

A: From the given data, the digits that are used for the formation of numbers are : 0,1,2,3,4,5 & 6

Q: the state department of transportation decides to change the plates to have three letters followed…

A: Given query is to find how many plates are possible if three latters followed by two digits.

Q: In Virginia, each automobile license plate consists of a single letter followed by three digits,…

A: 10×26×26×26×10×10×10

Q: How many numbers of four different digits each greater than 5000 can be formed from the digits 1, 2,…

A: Answer - How many numbers of four different digits each greater than 5000 can be formed from the…

Q: A typist has 5 letters and 5 addressed envelopes. In how many different ways can the letters be…

A:

Q: If the sum of two counting numbers is an even counting number, then the product of the two counting…

A: Suppose the two counting number is 5 and 5

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

A: The given digits are 0, 1, 2, 3, 4, 5, 6 4-digit numbers are formed using these numbers.

Q: If 7 numbers will be used to form telephone numbers, how many possible telephone numbers can be…

A:

Q: How many three digit numbers have the property that the sum of that number and the three digit…

A: How many three digit numbers have the property that the sum of that number and the three digit…

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

A: given digits;  0, 1, 2, 3, 4, and 5 total number of digits = 6 number of four-digits numbers can be…

Q: How many four-digit even numbers can you form from the digits 1, 2, 3 and 4?

A: We have to find the number of four-digit even numbers formed from the digits 1, 2, 3 and 4. Then we…

Q: A fast food restaurant advertises that it offers any combination of 8 condiments on a hamburger,…

A: The number is obtained as follows: The number of choosing none of the condiments on a hamburger:…

Q: How many distinct 8-letter words (real or imaginary) can beformed from the letters in the word…

A:

Q: How many four-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9 (a) if each digit…

A: We have to find total number of four-digit numbers :

Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6. If each number is used only…

A: Given: Numbers used = 2, 3, ,4, 5, 6 Numbers greater than 530 is required to be found. No digit is…

Q: How many EVEN 5-digit numbers can be made from the digits 2, 4, 5, 6, 7, 8, and 9?

A: Fundamental Counting Principle The Fundamental Counting Principle is a method used to determine the…

Q: What is the number of positive integers not larger than 210 and not divisible by 2, 3 or 7?…

A: Within 210, the number of integers that are divisible by 2= 210/2= 105  Within 210, the number of…

Q: How many 4-digit odd numbers can be made from the digits 0; 2; 4; 5; 8; 9 if the number has no…

A:

Q: How many seven digit telephone numbers are possible if the first two digits cannot be twos or zeros?

A:

Q: There are 9 female board members and 21 male board members. How many ways are there to make a…

A: We use combination to find number of way to make a committee.

Q: What is the sum of all 13-digit numbers?

A: What is the sum of all 13-digit numbers?

Q: How many numbers consisting of 5 digits can be made from 1,2,3,4,5,6,7,8,9?

A: How many numbers consisting of 5 digits can be made from 1,2,3,4,5,6,7,8,9?

Q: How many committees of six can be formed from 17 Republicans and 14 Democrats if three members of…

A: Given : 17 Republicans and 14 Democrats

Q: ) Students need to answer 8 out of 10 questions in mathematics exam. In how many ways can a student…

A:

Q: How many four-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5 and 7 if each digit can…

A: i) Since we need a four-digit number, the first digit can never be zero. Thus, the number of ways to…

Q: How many numbers consisting of five different digits can be made from the digits (0, 1 , 2, 3, 4, 5,…

A: ConceptPermutation = n!/(n-r)!Given digits are 0,1,2,3,4,5,6,7,8,9

Q: What two numbers have a sum of 8 and a product of 16?

A:

Q: Tony and Maria are two star-crossed lovers trying to get on a committee of 3 people. If there are 10…

A: In the question,Tony and Maria are trying to get on a committee of 3 people,Total number of eligible…

Q: The number of positive integers not exceeding 750 that are divisible by 3. 4. and 7 is: *

A:

Q: From 6 female employees and 5 male employees, how many groups of 5 employees can be organized…

A: There are 6 female employees and 5 male employees.

Q: Find the number of ways in which 5 economics books, 3 history books, and 2 mathematics books can be…

A: See the detailed solution below.

Q: There are 13 female board members and 17 male board members. How many ways are there to make a…

A: From the provided information, There are 13 female board members and 17 male board members. Total…

Q: Tony and Maria are two star-crossed lovers trying to get on a committee of 3 people. If there are 9…

A:

Q: How many of these numbers are even from the digits 0, 1, 2, 3, 5, 7 & 9 ?

A: Here we have to find  How many of these numbers are even from the digits 0, 1, 2, 3, 5, 7 & 9 ?…

Q: When you get to college you will be assigned a new Student Identification Number. If this number is…

A: Given, Student Identification Number has number is 9 digits long followed by 2 letters . We have to…

Q: What is the smallest sum possible sum of 25 consecutive positive integers which s a perfect square?

A: Let's take the 25 consecutive positive numbers as an Arithmetic Progression with first term a.…

Q: Find the number of different ways a grade A, B, C or D can be assigned to three students of a class…

A: Suppose we have three students x , y and z Now  x has 4 grade options y has 3( As one is already…

Q: How many even 4 digit numbers can be formed from the digits 1, 7, 2, 4, 6, 9, 3, and 0 if the…

A:

Q: Find the number of ways in which 6 teachers can be assigned to 4 sections of a math course if no…

A: Solution: 5. From the given information, there are 6 teachers and 4 sections.

Q: A license plate used 2 digits followed by two letters. If the numbers 1 and 0 can not be used in the…

A: Consider the provided question, Since, the numbers 1 and 0 can not be used in the digits. So, the…

Q: How many even three-digit numbers can be formed from the digits 1,2,3,5,6,8 and 9 if each digit can…

A:

Q: A witness to a hit-and-run accident tells the police that the license plate of the car in the…

A: The first letter has only one(A) chance, the second letter has 26 ways, the third letter has 26…

Q: How different committees can be formed from 10 women and 7 men if the committee many consists of 4…

A:

Q: Suppose Aaron is going to build a playlist that contains 14 songs. In how many ways can Aaron…

A: Given,total no.of songs=14

Q: What is the sum of the first 9,000 positive integers

A: topic - arithmetic sequence answer is 40504500

Q: there are 19 members on a board of directors. If they must form of a subcommittee of 4 members ,how…

A: Given that the total number of members on a board of directors is 19. They must form a subcommittee…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.