Find the minimum number of students that can be admitted to a college so that there are at least 15 students from one of the 50 states.

Q: What is the minimum number of balls that we need to draw to ensure that we get at least 3 balls…

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Q: A pencil case has 400 colored markers: 200 blue, 120 red, 50 green, and 30 yellow. What is the least…

A: Given problem Given that   A pencil case has 400 colored markers . 200 blue 120 red 50 green 30…

Q: 5. What is the minimum number of students, each of whom comes from one of the 72 provinces, who must…

A: We have to find What is the minimum number of students, each of whom comes from one of the 72…

Q: We want to distribute lunch boxes on 24 mosques, what is the minimum number of lunch boxes do we…

A: The minimum number of lunch boxes do we need to guarantee that the mosque that will get MOST of…

Q: A committee of 3 people is to be selected from 8 club members  find the number of committe that can…

A: Solution: From the given information, a committee of 3 people is to be selected from 8 club members.

Q: In the past, a college required students to use a 4 digit PIN (Personal Identification Number) as…

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Q: In a group of 100 people, each people needs to choose a number from 100 to 120. i)Prove that at…

A: Using the Pigeonhole principle we can prove the first statement. This principle states that if kn+1…

Q: There are 9 Canadian, 8 German, 6 Chinese, 10 French and 8 Russian students in a class. What is the…

A: We have, Total Nationalities = 5. So to guarantee at least four of the selected should have the same…

Q: find a set of smallest possible size that has both {3,4,7,8} and {1,5,6,9,10}

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Q: A box contains 5 yellow, 8 green, 11 blue, 11 purple and 15 white balls. What is the minimum number…

A: Number of yellow balls = 5 Number of green balls = 8 Number of blue balls = 11 Number of purple…

Q: Find the available number of passwords when using a 4 letter password with possible usage of…

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Q: How many subsets with an odd number of elements does a set with 12 elements have?

A: Given that a set contains 12 elements. We need to calculate the total number of subset with an odd…

Q: There are 35 different time schedules during which classes at the CIT University that can be…

A: There are 679 different classes (pigeons) but 35 different time periods(pigeonholes) in a…

Q: What is the minimum number of texts Ray must have before it makes sense to switch to the unlimited…

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Q: There are 8 Canadian, 7 German, 6 Chinese, 9 French and 9 Russian students in a class. What is the…

A: Given Data: No. of Canadian=8 No. of German=7 No. of Chinese=6 No. of French=9 No. of Russian=9

Q: Find the minimum number of students needed to guarantee that 11 of them were born in the same month.

A: Use the Pigeonhole principle to solve this problem.

Q: What is the minimum number of students, each of whom comes from one of the 17 regions, who must be…

A: We have students comes from 17 regions.  Now we will distribute no of students to each of 17…

Q: 4. Find the minimum number of students in a class to be sure that three of them are born in the same…

A: We have to apply the pigeon hole principle to solve this problem.

Q: Is there a formula to find the number of partitions in a set with n-elements?

A: Bell numbers, Bn, gives the number of partitions of a set with n elements It counts the number of…

Q: Assume that there are 13 pairs of black socks (çorap) and 8 pairs of blue socks in your drawer What…

A: In a single pair, there are two socks. In order to form a pair, at least 2 socks must be drawn.…

Q: There are 4 districts and 7 individuals available to carry out the survey. Assuming that no one…

A: There are 4 districts to be surveyed. There are 7 individuals available to survey the districts. The…

Q: In a city each person earns at most $5000 per month and every house is occupied by at most five…

A: HERE Given  Maximum earnings of of person = $5000 Maximum person in one one house= 5

Q: What is the minimal number of people needed in a class to ensure that there are two students with…

A: Given information: To ensure that there are two students with the same birthday (the same month and…

Q: The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee…

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Q: What is the minimum number of students, each of whom comes from one of 10 provinces who must be…

A: Let number of students that enrolled = n Number of provinces = 10 Number of pigeon holes = 10 Number…

Q: Suppose we wish to form a professional development committee with a selection pool of 12 students…

A: The question is bases on the concept of combinations we will use the following formula to calculate…

Q: During the annual conference of a professional organization, nine topics were proposed for…

A: Given- During the annual conference of a professional organization, nine topics were proposed for…

Q: How many subsets with an odd number of elements does a set with 10 elements have?

A: To find the total number of subsets with an odd number of elements of a set with 10 elements, first…

Q: What is the minimum number of cards that must be drawn from an ordinary deck of cards (52) to…

A: Given problem Given that   The minimum number of cards that must be drawn from a ordinary deck of…

Q: A bag contains 10 red marbles, 10 white marbles, and 10 blue marbles. What is the minimum number of…

A: From provided information; A bag contains 10 red marbles, 10 white marbles and 10 blue marbles. The…

Q: There are 9 Canadian, 9 German, 6 Chinese, 9 French and 9 Russian students in a class. What is the…

A: As given that there are 9 Canadian, 9 German, 6 Chinese, 9 French, and 9 Russian students in a…

Q: Consider a bag containing four red marbles, two green ones, one transparent one, three yellow ones,…

A: Total number of marbles = 4+2+1+3+3 = 13 Find the sets of five marbles containing 2 yellow marbles:…

Q: What is the minimum number resolution IV? (

A: It is given that here the two-level fractional factorial design is with resolution IV.

Q: The IECEP SLU Student Chapter is to have their Sportsfest. Thirteen teams were formed. Each team is…

A: Given: Number of teams is, N=13. Each team is to play with each other only once. The objective is…

Q: How many subsets is obtained from a set with 5 elements?

A: Given n=5

Q: Find the number of ways that a committee of 7 members can be selected from 8 sociologists and 6…

A: Combination is a technique to obtain the possible arrangements of listed items, where the order of…

Q: Construct an example of an IVP that satisfies

A: (a) Example of an IVP that satisfies the Existence and Uniqueness Theorem:

Q: Assume that there are 2 pairs of black socks (çorap),3 pair of pink socks, and 5 pairs of blue socks…

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Q: Colorado consists of 64 counties. What is the minimum number of students, each of whom comes from…

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Q: A lock consists of five parts and can be assembled in any order. A quality control engineer wants to…

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Q: What is the minimum number of students required in a discrete structures class to be sure that at…

A: As we have five grades: k=5 And the number of students: r=9 And we have to calculate: Nk=r N5=9

Q: golden section method

A: Hello. Since your question has multiple sub-parts, we will solve first parts for you. If you want…

Q: An access code consists of 2 letters of the alphabet followed by 4 digits. (Digits are 0, 1, 2, 3,…

A: There are 26 letters in the alphabet and there are 10 digits from 0 to 9. Thus, the 2 letters of the…

Q: Eight political committees must meet on the same day, but some members are on more than one…

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Q: a drawer contains 17 Black socks, 17 White socks, 17 Blue socks and 17 brown socks.  What is the…

A: A drawer contains 17 Black socks, 17 White socks, 17 Blue socks and 17 brown socks.

Q: there are 4 districts and 9 individuals available to carry out the survey. Assuming that no one…

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Q: What is the minimum number of students, each of whom comes from one of the 50 states, who must be…

A:

Q: There are 9 periods in each working day of a school. In how many ways can one organize 5 subjects…

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Q: 8. Find the minimum number of students needed to guarantee that 4 of them: (a) have last names which…

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Q: Calculate the number of subsets and the number of proper subsets for the set.  {1,3,5,7,11

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