How many days must be selected from the year to guarantee that at least 4 falls in the same month?12x

Q: Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how many…

A: Given: Number of sightseeing offered is, n=6. Number of days is, d=3. The objective is to find the…

Q: How many different passwords of 4 characters can be made using the numbers from 0 to 9 and the…

A: A password of four characters is to be made using the numbers from 0 to 9 i.e. 10 digits and the…

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: 4, and 6 if no digit is repeated in any number? a. b. repetitions are allowed?

A: We have to find the number of two digit numbers.

Q: 5 identical copies of a movie will be stored on 20 computers such that each computer has at most 1…

A: Given: 5 identical copies of a movie will be stored on 20 computers

Q: How many days must be selected from the year to guarantee that at least 4 falls in the same…

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Q: Find S, the sum of first 15 Natural numbers 15

A: We have to find sum of first 15 Natural numbers.   S15? Solution :  As we know that the sum of first…

Q: How many permutations π of [10] satisfy π^5 = 1?

A: The given set is 10=1,2,3,…,10. Therefore any permutation π of 10, is bijective function from the…

Q: Be able to demonstrate the fact that at least 10 of the 64 days selected must occur on the same…

A: let we have selected 64 daysThen day 1 is any one week day from 7weekdaysLet day 1 is weekday xAfter…

Q: Assume that you select digits from the set {1,2,3,4,5,7,8} to form a number between 10 and 800. (1)…

A: given set of digits is  {1,2,3,4,5,7,8}  and the range of numbers is 10 to 800. There would be 2…

Q: How many computer passwords of length 3 you can make out of given 5 characters a. if repetition of…

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Q: A student is allowed to select at most n books from a collection of (2n+1) books. If the total…

A: We will solve the problem

Q: uppose the sap is collected in gallon buckets that hang under each tap, and that the maple syrup…

A: It takes 40 gallons of sap to make one gallon of syrup The sap required for the production of 30,000…

Q: How many 8-bits strings have exactly three 1's?

A: Given that  8 bits strings have exactly three 1 s is

Q: Only 3 ships dock on a remote port. One ship docks every other 8 days, the second ship every 10…

A: We have to find out the number of days the port is empty i.e the port is free

Q: 1.How many license plates consisting of 6 digits (0 to 9) have their digits in strictly increasing…

A: Given that, How many license plates consisting of 6 digits (0 to 9) have their digits in strictly…

Q: Consider a list of randomly generated 2-letter "words" printed on a paper. The letters cannot be…

A: Total number of different 2 letter word without repeated words is 26×25=650.(a)At least how many of…

Q: Assume that there are 2.9 million people in the United States named David and 366 possible birthdays…

A: Given- Assume that there are 2.9 million people in the United States named David and 366 possible…

Q: There are m months in a year, w weeks in a month and d days in a week.How many days are there in a…

A: Number of days in 1 week = d Number of days in w weeks = d×w…

Q: Form a 26-letter word by randomly permuting the 26 letters of the English alphabet. We say that this…

A:

Q: 4. There are 53 different time periods during each class at a university can be scheduled. How many…

A: There are 53 different time periods during each class at a university can be scheduled. We need to…

Q: Each customer in a certain bank has a PIN number, which is a sequence of four digits. Show that if…

A:

Q: 4. Find the largest number of points which a foot ball team cannot get exactly using just 3-point…

A: For our company rules I solve only first question. Please repost other parts.

Q: Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how many…

A: Number of sightseeing tours for one day are 6. Number of days for the tour is 3.

Q: 7. How many 10 bit strings have an equal number of 0's and 1's? How many have 8 (and only 8)…

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Q: PLEASE HELP, i really need to understand these questions before my finals. pleaseee?

A: The Pigeonhole Principle:  If there are n+1 objects and it is required to place then in n boxes then…

Q: A lottery game requires that 4 different numbers are picked from 1 to 9. If someone picks all4…

A:

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: 93% of all dolphinesare cured of a particular bacterial infection. if 6 dolphines are treated and 3…

A:

Q: A passcode contains four digits from the digits 0-9. How many different passcodes can be made if no…

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Q: How many collections are possible? How many of these collections contain HPQ but not SAGE? How many…

A: Given, Purchasing 3 tech stocks and 2 health care stocks from those stocks To find The number of…

Q: a) Among 82 people at least how many were born in the same month? Answer = b) Assuming that no one…

A: Introduction: According to the pigeonhole principle, if n items are placed in m containers, with n…

Q: Prove that among 100 people, at least 9 were born in the same month.

A: We have a group of 100 people. We need to prove that at least 9 were born in the same month. We will…

Q: How many combinations are possible? Assume the items are distinct. 19 items chosen 19 at a time…

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Q: Find the sum of the first five natural even numbers using sigma notation.

A: We have to find sun of first 5 even natural numbers.

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 6-permutations of [15] have their digits in increasing order?

A: Permutation is a technique to obtain the possible arrangements of listed items in a linear order.…

Q: How many people must be selected to guarantee that at least 4 have a birthday in the same month?

A: This is an application of pigeon hole principle. According to pigeon hole principle, if there are n…

Q: How many people are needed to guarantee that at least two were born on the same day of the week and…

A: There are 7 days in a week and 12 months in a year.

Q: A telephone call center where people place marketing calls to customers has a probably of success of…

A: Introduction: Denote X as the number of successful calls, among the n calls. Each call may be…

Q: Number of circular permutations of different .!things taken all at a time is (n-1)

A:

Q: How many different calendars are possible for a year?

A: Here Given  There is two type of years LEAP and NON LEAP Year

Q: 11 Given the digits 6, 7, 8, 9, a. How many four number digits can be formed if there's no…

A: Given digits are  6, 7, 8, 9 each parts are solved below.

Q: 1. Will there be at least five people who celebrate their birthday in the same month Yes No

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: How many two-digit numbers can be formed using the digits from {2, 4, 6} if the following is true.…

A: Given: The digits are {2, 4, 6} Number of ways to form two-digit number without repetition…

Q: 8. If a clock strikes the appropriate number of times on each hour, how many times will it strike in…

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Q: How many 10-bit strings contain 5 or more 1's?

A:

Q: Suppose a telephone number consists of a sequence of seven digits not starting with a 0 or 1.  a.…

A: From the provided information, The telephone number consists of a sequence of seven digits. a) If…

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