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

Q: A fleet of nine taxis is to be dispatched to three airports in such a way that two go to airport A,…

A: Given, A fleet of 9 taxis is to dispatch to the three airports A, B, and C also, 2 go to A, 6 go to…

Q: 4. How many subsets are there of {1, 2, 3, 4, 5}? How many contain at least three elements? How many…

A: Given set is S=1,2,3,4,5 Since we know that, if a set contains n elements, then total number of…

Q: How many distinct ten-digit passwords are possible if you must use at least one 26 lower case letter…

A: Given: you must use at least one 26 lower case letter from {a, b, . . . , z}, at least one 26 upper…

Q: 2) Each type of machine part made in a factory is stamped with a code of the form…

A: We can use :- 26 letters, 10 digits, 10 digits (as digits can be repeated)   Total number of…

Q: 1 red, 1 blue, 1 black, 1 yellow and 1 white car are all waiting at the traffic lights behind each…

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Q: There are five distinct computer science books, three distinct mathe- matics books, and two distinct…

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Q: How many five-digit numbers are there for which each digit is either equal to both adjacent ones, or…

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

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Q: Let $n$ be a positive integer. Among C(2n,0),C(2n,1),..., C(2n,2n), C(2n,n) is the largest. True…

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Q: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

A: Solution-:

Q: If seven integers are chosen from between 1 and 12 inclusive, must at least one of them be odd? Why?

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Q: (a) Show that if seven integers are selected from the first 10 positive integers, there must be at…

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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: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: A sales assistant is hanging  11  sweaters on a rack. He has  5  green sweaters,  3  pink sweaters,…

A: In how many distinct orders can the sweaters be arranged if two sweaters of the same color are…

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

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Q: How many different words with or without meaning can be formed with the letters of the word…

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Q: Assume that product codes are formed from the letters X, T, and R, and consist of 6 not necessarily…

A: Given,  Product codes are formed from the letters X, T, and R, and consist of 6 not necessarily…

Q: Assume that the committee consists of 13 members including Bill. The same three offices are to be…

A: Given, Assume that the committee consists of 13 members including Bill. The same three offices are…

Q: A bank of 9 movies is chosen from for a movie marathon in which 3 movies will be played in a…

A: Given that,  There are 9 movies in the bank. According to the given condition, 3 movies are played…

Q: How many positive integers less than 1000 are divisible by 5? How many positive integers less than…

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: How many positive integers between 100 and 999 inclusive   d) are not divisible by either 3 or 4?…

A: The set: A∪B contains all the elements that are present in set A or B. The set A-B contains all the…

Q: In how many ways 4 fruits (of any type) can be picked up from a basket of fruits containing 3 types:…

A: Given Information Basket contains 3 types of Fruits: Apples, Oranges and Pears 4 fruits is to be…

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: In how many distinct orders can the sweaters be arranged if two sweaters of the same color are…

A: HERE GIVEN , A sales assistant is hanging 11 sweaters on a rack. He has 5 green sweaters, 3 pink…

Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: Refer to a set of five distinct history books, three distinct biology books, and two distinct…

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Q: How many integers in the set {1,2,3,4, ..., 200} is divisible by at least one of the primes 2, 5 and…

A: Just use inclusion-exclusion principle for three sets.

Q: so the S and T remain next to each other (though not necessarily in that order, so ST or TS are both…

A: Consider as S and T as one letter. So now the total number of English alphabet which needed to…

Q: Prove that if the sum of the digits is subtracted from a natural number, then the result is…

A: let us assume the number to be three digit number xyz therefore, xyz=100x+10y+z sum of digits will…

Q: How many strings of 7 decimal digits are there, such that at least one of the digit is odd?

A: There are total 10 decimal digits, among which 5 are odd. Since repetition of digits is allowed,…

Q: How many different ways can you arrange 2 letters from a set of 3 letters {L, S, U} such that…

A: There are 3 distinct letters. We must find the number of ways 2 of these letters can be arranged…

Q: 17) How many elements are in the union of four sets if the sets have 100, 150, 250, and 400…

A: Here, n(A)= 100, n(B), 150, n(C)=250, n(D)=400 n(A∩B)=15, n(A∩C)=15, n(A∩D)=15, n(B∩C)=15,…

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 four​-digit numbers may be formed using elements from the set {1, 2, 3, 4, 5, 6, 7} if no…

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Q: ) How many 4 digit numbers that are divisible by 10 can be formed from the numbers 3, 5, 7, 8, 9, 0…

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

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

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: 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: 1- The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit…

A: NOTE- AS PER POLICY I  HAVE CALCULATED FIRST MAIN QUESTION ONLY. Here Given 4 digits 1,2,3,4

Q: How many 5-digit numbers can be formed using the digits 2, 3, 4, 5, and 6 without repetition? With…

A: To find how many   5 digit number  can be formed using  2,3,4,5 and 6 without  repetition and then…

Q: How many 5-tuples (x1, x2, x3, x4, X5) of positive integers from 1 to n are there? How many 5-tuples…

A: Since you have asked multiple questions, we will solve the Question Q1 (a) and (b) and (c) for you.…

Q: Prove that if n > 1 is a number with φ(n) = n/k, then k = 2,3.

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Q: 2) How many elements are in the union of 5 sets if the sets contain 10,000 elements, each pair of…

A: Given that there are 5 sets and sets contains 10,000 elements, each pair of sets has 1000 elements,…

Q: 4. How many positive natural numbers less than 1000 are neither divisible by 3 nor 5 nor 7 nor 11.

A: Let U={1,2,3,...1000} n(U)=1000 A={a∈U/ x is divisible by 3}A={3,6,9. . .…

Q: . Find the number of permutations of the letters of the word ‘REMAINS’ such that the vowels always…

A: We can solve these questions using given details

Q: In how many ways can a person select seven party guests from 12 women  if he is to avoid having a…

A: Here we will use the concept of Combination

Q: A restaurant sell features a burrito bar in which a customergets to choose one of 2 different kinds…

A: As per bartleby guidelines only one question is answered please upload the other one separately…

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…