n how many distinct ways can the digits in the number 1,243,520,326 be arranged? (If there are any zero digits then assume they can be placed in any position)

Q: 3. How many 4-digit positive integers are there that are even or contain no O's?

A:

Q: 3) Sarah writes down random positive integers when she gets bored. Prove that if Sarah writes 1001…

A: Given:  Sarah writes 1001 numbers.  Since there are 10 digits, i.e., there are only 103 = 1000…

Q: How many phone numbers are possible in the (770) area code for the form ABC-XXXX if: A is restricted…

A: Here,the phone  number  is in the form ABC-XXXX. Given that A is restricted  to 1-9, that is we can…

Q: . How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by…

A:

Q: Using the digitd 3, 4, 5, 6, 7, 8, and 9, how many 4-digit numbers can be constructed if the number…

A: Solution: From the given information, the digits are 3, 4, 5, 6, 7, 8 and 9. Here, the numbers with…

Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly three 0s, five 1s,…

A: Total number of digits are 12 Given there are three 0's , five 1's and four 2's

Q: In a set of 2 positive integers, how many ways it can be chosen in less than 50? 1.

A:

Q: (a) How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible…

A: As we want our 3-digit number to be divisible by 5, the number 5 will be fixed on the unit's place…

Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, and 9, which are divisible by 5,…

A: Given information- We have given the digits- 2, 3, 5, 6, and 9. We have to form the 3 digits numbers…

Q: Find how many positive integers with exactly four decimal digits, that is, positive integers between…

A:

Q: 8. In how many ways can four integers 1, 2, 3, and 4 permute taken a. taken two at a time b. three…

A: Given, Four integers 1,2,3 and 4 permute taken

Q: a) How many 3-digit positive integers are there with odd digits?

A:

Q: How many integers from 1 to 1000: a) Are divisible by 7? b) Are divisible by 7 but not 11? e) Are…

A: a) From 1 to 1000 there are 1000 numbers. Now, 1000/7 = 142.86 So, there are 142 multiples between 1…

Q: 2. In how many ways can three numbers be selected from the numbers 1, 2, ... , 300 such that their…

A: This problem is solved using the concept of permutation and combination. please find step by step…

Q: (b) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 and 8 such…

A: Given Digits: 0,1,2,3,4,5,6,7 & 8

Q: 6. Calculate the number of different six-digit numbers which can be formed using the digits 0,1, 2,…

A:

Q: In how many distinct ways can the digits in the number 1,238,229,168 be arranged?

A: We have to find in how many ways the number  1,238,229,168 can be arranged.

Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly four 0s, four 1s,…

A: The 12 ternary digits can be arrange in 10! ways, in which exactly four 0s, four 1s, and four 2s can…

Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

A:

Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: 4. How many 5 digit numbers can be formed if a) the digits 2-8 are available and there must be at…

A: 4. It is required to form 5 digit numbers under two different sets of conditions.

Q: How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

A:

Q: A) How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Note :- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: a. If there are 8 different colors of foot balls are available in a sports shop, in how many wavs…

A:

Q: 1)How many integers between 1000 and 2000 are divisible by at least one of the integers 3, 5 and 7?

A: Introduction: In mathematics, integers are the sum of positive and negative numbers. Integers are…

Q: 27. Determine the number of n-digit numbers with all digits odd, such that 1 and 3 each occur a…

A:

Q: 3. If а, 1000". Find N E I, the set of positive integers, such that an+1 N). n!

A: Given an=1000nn!. We have to find the N∈I such that an+1<an, n>N. For n=1 a1=100011! For n=2…

Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?

A:

Q: In how many ways can the digits in the number 2,767,676 be arranged? There are ways to arrange the…

A: In this number, there are 1 two. 3 sevens 3 six. And total (1+3+3)=7 digits

Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if…

A:

Q: 4.The set of integers from 1 to 10 that is divisible by 3.

A:

Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly hree Os, five 1s,…

A: Strings of 12 ternary digits, 3 possibilities for each digit in the string, gives a total of 3^12 =…

Q: 11:54: If n EN andn<2000, how many numbers n have the property that the sum of the digits of n and…

A:

Q: 25) How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if…

A: This question is taken from the permutation and combination since the question is multiple hence we…

Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters co can be generated?…

A: Given: There are 7 letters A, B, C, D, E, F, G

Q: How many 5-digit numbers can be made from the digits 1 to 9 if: a) Repetition of digits is allowed?…

A: Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART ONLY

Q: How many integers between 100 and 400 contain the digit 2? There are integers between 100 and 400…

A: Numbers between 200 and 299 contains 2 So total integers = 100 Numbers between 120 – 129 contains 2…

Q: 1. How many 3-digit numbers can be forms from the four digits 0,1,2,3 if: a) no two digits are to be…

A: according to our guidelines we can answer only three subparts, or any question and rest can be…

Q: 3. How many different license plates are possible if a state uses (a) Two letters followed by a…

A: (a).We have  (0,1,2,...,9) 10 digits , and 26  letters (A,B,C,.....,Z). Repetitions of digits and…

Q: Prove that 8 divides 9" – 1 whenever n is a natural number. For each natural number n, let P(n) be…

A: To prove that  8 divides 9^n-1 whenever n is a natural

Q: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

A:

Q: How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never there in the…

A:

Q: How many integers from 1 to 500 are divisible by at least one of  the numbers 3, 4, 5?

A: Given :  Integers from 1 to 500 Total numbers  = 500 So to calculate the number of divisors, we will…

Q: In how many ways can 4 t-shirts, 7 denims, and 4 coats be arranged in a clothing store shelf section…

A:

Q: 4. For natural numbers n and k, prove (C) - ()

A: We have to prove

Q: -Each student at State University has a student ID number consisting of five digits (the first digit…

A:

Q: How many three numbers with no repeated digits, can be formed by the use of the digits 0, 2, 3, 4,…

A: here AS PER GUIDELINES I HAVE CALCULATED 3 SUBPARTS  Three digit number is formed using digit…

Q: We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have…

A: Here we will use permutation /arrangement and combination / selection  Number of way r object can be…

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.