Using the pigeonhole principle How many numbers must be selected from the set {1, 3, 5, 7, 9, 11, 13, 15} to guarantee that at least one pair of these numbers add up to 16?

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 ways are there to form a subset of [n] of size k with the property that each selected…

A: Given n=8 k=3 4 ways 1,4,7,1,4,8,1,5,8 and 2,5,8 Find How many ways are there to form a subset of n…

Q: How many books must you choose from among a collection of 7 mathematics books. 18 books of short…

A: Given information  No of mathematics book = 7 No of short stories books = 18 No of chemistry books =…

Q: Pigeonhole principle 1. In a group of 21 people, there is a ____ chance that at least two of them…

A:

Q: Given nine sets {5,15,16,18}, {2,19,21},{1,9,14,16},{1,6,20}, {3,16,21},{5,14,20,21},…

A: given : {5,15,16,18}, {2,19,21},{1,9,14,16},{1,6,20}, {3,16,21},{5,14,20,21},…

Q: Using the extended pigeonhole principle, show that if there are 30 students in a class, then at…

A:

Q: Using only the digits { 1, 2, 3, 4, 5, 6} how many three digit numbers can be formed under the…

A: The first digit has 4 options which are, 1, 2, 3, 6. The second digit can have 5 options (one option…

Q: Toss 5 coins 20 times simultaneously and observe the number of heads that will occur. The possible…

A: Given:  There are 5 coins tossed 20 times simultaneously.  X = number of heads  X is a random…

Q: An organization sponsored a raffle where they were to sell all 500 tickets sequentially numbered…

A:

Q: A jar contains 10 balls numbered 1, 2, 3, ... , 10. We draw 15 balls from the jar, one after…

A: Given information: Given that the jar contains 10 balls numbered from 1, 2, 3, … , 10. The…

Q: Computer passwords are to consist of a string of six symbols taken from the digits 0,1,2, ... ,9 and…

A: Number of digits=10 Number of lower case letters=26 Total number of symbols=10+26=36 Length of…

Q: green A store sells rubber balls in 4 different colors: red, yellow, blue, and If the store has a…

A:

Q: b . What is the minimum number of cards that must be drawn from an ordinary deck of cards to…

A: b)i) There are 13 ranks. [J,K,Q,A,2,3,4,5,6,7,8,9,10] If we have 2 cards from each rank , then we…

Q: four or five-digit PIN is to be selected from the ten digits 0,1,2,3,4,5,6,7,8,9. How many 4-digit…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: Counting numbers are to be formed using only the digits 2, 1, 4, 8, 9, 6, and 3. Determine the…

A: The objective is to determine the number of different possibilities for​ two-digit numbers which are…

Q: 2. even numbers are in their natural positions. Determine the number of permutations of {1, 2, 3, 4,…

A: Here we use combination rules. And set theoretic rules.

Q: License plates in Edmonville consist of a digit other than 0 or 9, followed by any 2 letters, which…

A:

Q: Counting numbers are to be formed using only the digits 9,4,8,1 and 2. Determine the number of…

A:

Q: ct proper subsets are there of the set N = {3, 43}?

A: The number of elements in the set are 2 ( which are 3, 43)

Q: How many combinations are possible? Assume the items are distinct. 9 items chosen 4 at a time…

A: Combinations: The number of combinations of r items selected from n items is, nr=n!n-r!r! It is…

Q: How many strings of 7 English letters are there that start and end with the letter T and contain at…

A: Given, we have to make 7 letters string that  will start and end with T    And the string have at…

Q: Six cards are drawn from a deck of playing cards find the number of ways of selecting all cards are…

A: Solution: Note: Hello! As you have posted 2 different questions, we are answering the first question…

Q: A telephone number consists of 7 digits. How many phone numbers are possible if the first digit is…

A: The formation of a telephone number is a significant use of counting. A telephone number consists of…

Q: A password a string that consists of 4 digits from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, followed…

A:

Q: Using the set {1,3,4,6,7,8,9}, how many odd numbers can we construct between 100-999 if no element…

A: An odd number is determined by the unit digit. If the unit digit is an odd number, then the number…

Q: A set contains 7 distinct elements. How many subsets can be formed from the elements of S that…

A: Use combination formula

Q: Use pigeonhole principle 1. How many numbers must be selected from the set {1, 3, 5, 7, 9, 11, 13,…

A:

Q: Tennis balls are randomly toss into one of five trays. Determine the number of balls needed to…

A:

Q: A PIN-number for a credit card consists of a sequence of 4 digits chosen from the set…

A: Given the set {0,1,2,3,4,5,6,7,8,9} We find the 4 digits different PIN number

Q: A card game uses a special deck where each card has a number and a color. The numbers range from 1…

A: There are numbers range from 1 to 12. So total of 12 numbers. The colors are red, orange, yellow,…

Q: 5. Four married couples have bought 8 seats in the same row for a concert. In how many. different…

A: a). The number of possible permutations of n object is n!. So, the number of permutation for 8…

Q: What is the set N of all natural numbers?

A: Set of all integers: ℤ={.......,-3,-2,-1,0,1,2,3.......} Set of all positive integers…

Q: (a) How many seven-digit telephone numbers are possible if the first digit must be nonzero? possible…

A: a) Seven places among which first place is non-zero. so, First place has 9 options 1 or 2 or 3…

Q: 1. How many ways can you choose 4 numbers from the set p = {4, 6, 8, 10, 12} or 3 numbers from the…

A:

Q: A certain combination lock allows the buyer to set any combination of nine letters, with repetition…

A: We use here combination for counting number of locks can be make.

Q: a) A user's password to access a computer system consists of four digits followed by five lowercase…

A:

Q: A fruit grower packs apples in boxes. Each box contains at least 220 apples and at most 231 apples.…

A:

Q: 3. How many 4- digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 it: a) no…

A: Given many 4-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7

Q: A basket holds a set of balls. Each ball is red, green, or blue. How many balls must there be in the…

A: We have given that A basket holds a set of balls. Each ball is red, green, or blue. How many balls…

Q: 6. Each telephone number in a city consists of 7 digits. а. How many telephone numbers are possible…

A:

Q: set of two - digit numbers obtained from the digits 1

A:

Q: 5 numbers are to be chosen from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} How many ways can 5 (not necesarilly…

A:

Q: How many subsets of 3-elements can be formed from the set { a, b, c, d, e }?.

A: Given set a,b,c,d,e Since we have to select 3 elements from the set of 5 elements to get subset of 3…

Q: How many four-digit even numbers are possible if the leftmost digit cannot be zero? Repitition is…

A: The possible total ten numbers are {0,1,2,3,4,5,6,7,8,9}.Since the left most digit cannot be zero,…

Q: estion 24 According to the Pigeonhole Principle, among any group of 8 people, there must be at least…

A: according to pigeonhole principle

Q: Using the inclusion-exclusion principle, find the number of integers from a set of 1-100 that are…

A:

Q: a) Using only the numbers 0, 1, 2, 5, 6, 7, and 8, determine how many 4 digit natural numbers are…

A: How many 4 digit natural numbers are possible using 0,1,2,5,6,7,8

Q: Using the digits 1, 2, 3 and 5, how many 4 digit numbers can be formed if a) The first digit must be…

A:

Q: . Using inclusion-exclusion find the number of ways to put 9 pairs of people in a ne of 18 so that…

A:

Q: Cards are drawn one at a time, without replacement, from a standard deck of 52 cards until all 4 of…

A: Given Standard deck of 52 cards until all 4 of the aces are drawn