In how many ways can you rearrange the letters of the word 'FACTOR'. Show your computations.

Q: How many ways can the letters of the word MAILBOX be arranged in a row if the letters ILB must…

A: Consider the word "MAILBOX" Given: "ILB"  must remain together (in order) To find: The number of…

Q: How many numbers in the set {1, 2, 3, ..., 346} are divisible by 5 or 7 ?

A: In the given problem we have to find how many numbers in the set 1, 2, 3, . . ., 346 are divisible…

Q: If a number is not divisible by 6, then it is not divisible by 3. true or false

A: If a number is not divisible by 6, then it is not divisible by 3.

Q: How many 12-digit numbers can be formed from 4 ones, 2 twos, 3 fives, and 1 six and 2 nines?

A: We want to find 12 digit number with given digits.

Q: Find the number of the permutation of 8 different things taken 3 at a time

A:

Q: Show that a number with 30 digits cannot have more than 100 prime factors.  

A: Prime factor: A factor of a number which is a prime number. For example: consider a number 26. The…

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: How many different ways can 5 calculators be arranged in the cabinet from a group of 15?

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

Q: In how many ways can 9 gifts be divided between 4 children if the eldest child is to receive 3 gifts…

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Q: Write down a perfect square number consists of three digits and then Find the square root of it…

A: When any number multiplied itself twice, the obtained number is known as perfect square number. i.e…

Q: In how many different ways can four pennies, three nickels, two dimes and three quarters be arranged…

A: Pennies =4  Nickels = 3 dimes= 2 quarters = 3 The objects are 4 pennies, 3 nickels, 2 dimes and 3…

Q: How many 5-digit numbers can you make using the digits 0-9 without repeating the digits? *

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Q: What is the sum of the two largest prime factors of 770?

A: You need to express in terms of prime factors.

Q: What is the smallest positive integer that has 6, 8, and 10 as factors?

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Q: Create your own worded problems related to Permutations. How can Permutation be an important…

A: Hi I have provided you the detailed information about the concept of permutations. Hope it will…

Q: In how many ways can you arranged 2 Math books, 3 Science books and 3 English books if only one book…

A: The total number of mathematics books are 2. The total number of science books are 3. The total…

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 4-digit numbers can you make using the digits 1-9 without repeating the digits? *

A: We will solve the problem.

Q: A prime number that is a common factor of 20 and 32 ?

A: Consider the given positive integer 20 and 32.In order to find the prime factor of 20 and 32, first…

Q: How many different "words" can be formed by rearranging the letters in the word EXAGGERATED?

A: We have find out number of words

Q: How many ways can 8 CDs be arranged on a shelf?

A: To be found : Number of ways 8 CDs can be arranged on a self.

Q: The number of 3-digits numbers that can be formed without repetition from the numbers 2.3.5.7 and 8…

A:

Q: how many 6 digit numbers can be formed, if at the place of hundred thousand there are allowed two…

A: Yes your step is right.Hundredth thousand place can be chosen in 2 ways. And hundredth place can be…

Q: How many ways can 8 DVDs be arranged on a shelf?

A: We can arrange 8 DVD's in 8! ways.

Q: How many different numbers of five digits can be made using the digits 2,2,3,3,3?

A: The objective is to find how many different numbers of five digits can be made using the digits…

Q: How many four-digit odd numbers less than 7000 can be formed using the digits 2, 3, 5, 7, 8, and 9?

A: To determine four digits odd number less than 7000

Q: How many positive numbers less than 300 are divisible by 7 but not 5?

A: We need to find positive numbers less than 300 that are divisible by 7 but not by 5. First count the…

Q: How many ways can the letters of the word MAILBOX be arranged in a row?

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 11. Explain what is a factorial and show an example of how to compute it.

A: A factorial of a number is the product of all positive integers less than or equal to the given…

Q: How many baseball teams of 9 members can be formed from 14 players?

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Q: The World Health Organization is conducting a study of environmentally related diseases. In how many…

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Q: Explain why it is convenient to write the expression for the number of possible permutations in…

A: It is efficient and time saving, imagine if you want to write 4! in its entire multiplication form…

Q: Find the largest eight-digit number made up of the digits 1, 1, 2, 2, 3, 3, 4, and 4 such that the…

A: Given digits are 1,2, 3, 4.Given conditions is 1s are seperated by one digit,2s are seperated by two…

Q: How many different 4-digit numbers can be formed from the numbers 2, 4, 5, and 8 if no digit is…

A: How many different 4-digit numbers can be formed from the numbers 2, 4, 5, and 8 if no digit is…

Q: How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?

A: Consider the given situation in the problem, we have four groups in which we have to make choice to…

Q: In How Many Ways Can 7 Toys Be Divided Among 3 Children If The Youngest Gets 3 Toys And Each Of The…

A:

Q: Find the number of positive integers ≤ 1000 that are not divisible by 5, 13, or 31?

A: .  Symbol of Greatest Integer Function  To Find: Number of positive integers ≤ 1000 that are not…

Q: What is Prime Factorization

A:

Q: How many different numbers of 3 digits can be formed from the numbers 0, 1, 2, 3, 4, 5, 6 7, 8?

A:

Q: How many ways can you rearrange the numbers 1, 2, 3, 4, 5, 6, and 7? *

A:

Q: How many four-digit numbers can be formed from the numbers 1, 3, 4, 6, 8, and 9 if repetition of…

A:

Q: IN HOW MANY WAYS CAN 5 MATH BOOKS AND 3 ART BOOKS CAN BEARRANGED IN A ROW, IF NO TWO ART BOOKS WILL…

A: We can first place the 5 math books in 5!= 120 ways. When they are placed. Then we have 6 gaps…

Q: How many ways can four of the letters of the word MAILBOX be selected and written in a row if the…

A:

Q: How many zeroes are at the end of 25! (= 25 factorial)?

A: The given number is 25!.  Now, we need to find the number of zeros at the end of 25!.

Q: How many ways there to rearrange the letters in the word "excellence" (including the original word…

A:

Q: How many ways can my daughter put 50 pairs of shoes on 4 dolls?

A: Combination :  The number of ways to choose a sample of k elements from a set of n distinct objects…

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: Find the sixth term in the pattern 3,3,6,9,15

A:

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.