From a club of 16​people, in how many ways can a group of six members be selected to attend a​ conference?

Q: A group of four students studying for a bar exam has formed a study group. Each member of the group…

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Q: |In how many ways can a photographer at a wedding arrange 6 people in a row from a group of 9…

A: Combination is the arrangement of data without any order. It can arrange data from the sample from…

Q: How many ways are there to arrange 12 identical apples and five different oranges in a row so that…

A: Here, arrange 12 identical apples and five different oranges in a row so that no two oranges will…

Q: Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to…

A: Three married couples are to be seated in a row having six seats in a cinema hall. We have three…

Q: In how many ways can a commitee of 9 students be chosen from 8 juniors and 10 seniors if there must…

A: Given data: 8 juniors and 10 seniors

Q: In how many ways can a hostess select 6 luncheon guests from 10 women, if she is to avoid having a…

A:

Q: In a certain state license plates are formed by choosing 2 letters followed by 4 digits without…

A: Solution: Let L1 and L2 be the first two letters of a license plate.  For L1 we have 26 options…

Q: From among the 36 teachers in a college, one principal, one vice-principal and the teacher-in-charge…

A: It is given that there are 36 teachers in a college. We have to appoint one principal, one…

Q: how many ways can Dr. Yes invite 8 of his friends if he has to invite at most 4 at a time?

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Q: how many ways can a party of 8 people be seated in a circular table if 3 of them insist on sitting s

A: Given data,In a party there are 8 peoplen=8how many ways can a party of 8 people be seated in a…

Q: From a club of 16 people, in how many ways can a group of five members be selected to attend a…

A: Given Data: The number of people in the club is: n=16 The number of members required is: x=5 The…

Q: a contractor builds homes of 9 different models and presently has 3 lots to build on. In how many…

A: Given: A contractor builds homes of 9 different models and presently has 3 lots to build on.

Q: If repetitions are not permitted, how many 3-digit even numbers can be performed from the six digits…

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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: 2. In a group of 700 people, must there be 2 who have the same first and last initials? Why?

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Q: Ten prizes are to be given to 10 different people in a group of 16. In how many ways can a first…

A: Given that there are 10 prizes and 16 people.  So the first prize can be given to any of the 16…

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: In how many ways can you make any arrangement of 3 vowels and 5 consonants taken from the alphabet…

A: In how many ways can you make any arrangement of 3 vowels and 5 consonants taken from the alphabet…

Q: Suppose 12% of students chose to study French their freshman year, and that meant there were 21 such…

A: Given: Suppose 12% of students chose to study French their freshman year and  that meant there were…

Q: In how many different ways can the director of a research laboratory choose two chemists from among…

A: Solution: Given information: Chemists applicants = 11  Physicists applicants = 7   To choose 2…

Q: How many five​-digit numbers can be formed with the first two digits odd and the last three digits…

A: The number of digits need to be formed is five. The first two digits are odd and the last three…

Q: How many ways to arrange 7 books on the shelf exist if two definite books are not placed together?

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Q: A student wants to buy 3 CDs. Assume that they are interested in 6 CDs featuring the piano, 4 CDs…

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Q: In how many ways can first and second prize be awarded in contest with 100 people, assuming that…

A: There are 100 students in the contest.

Q: How many strings of Seven English letters are there A) That contains no vowels, if letters can be…

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Q: In how many ways can a committee of 4 executives be organized from 15 executives.

A: There are 15 executives. We have to make a committee of 4 executive.

Q: In how many ways can a group of 5 girls be selected from 8 if the eldest girl is included in each…

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: In an apartment complex with 10 mailboxes, in how many ways can a mail carrier distribute 10 letters…

A: The formula for finding the  one addressed to each box such that at least one letter is put into the…

Q: A committee of 5 consisting of 3 girls and 2 boys is to be chosen from a class with 15 girls and 10…

A: Given: Total Number of Girls=15Total Number of Boys=10Commitee required 5 candidate in whichNumber…

Q: In how many ways can 8 students be seated in a row if two particular students must never be seated…

A: In the given problem we have to  find in how many ways can 8 students be seated in a row if two…

Q: how many ways are there if a teacher has to select 2 students from a group of of four to represent…

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Q: How many different phone numbers can be formed if it must have 7 digits and cannot start with 0 or 1…

A: Given data: phone numbers can be formed if it must have 7 digits and cannot start with 0 or 1 and…

Q: In how many ways can a hostess select six luncheon guests from 10 women if she is to avoid having a…

A: Combination and permutations

Q: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

A: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

Q: How many different​ three-digit numbers can be formed using the digits 4, 5, 2, and 8 with​…

A: The given digits 4,5,2,8.  and repetition allowed

Q: A committee consists of 5 people Smith,Jones,Clark,Brown and White in how many ways can the members…

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Q: A committe of 5 members is to be formed out of 6 gents and 4 ladies. In how many ways this can be…

A: Given: Total Gents = 6 Total Ladies = 4 Required 5 members committee for the at least two ladies

Q: How many ways can a president, vice-presidnt, secretary, and treasurer be chosen from a club with 8…

A: In this problem, order is important because once someone is chosen as a position they can not be…

Q: How many different five-letter code words are possible from the first ten letters of the alphabet if…

A: 5 letter codes out of first 10 letter of the alphabet ?if 1st letter can't be a vowel and adj…

Q: How many words can be formed by permutation of the letters of the word DEPRESSION such that each…

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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 student is given a reading list of ten books from which he must select two for an outside reading…

A: Given that the student has a list of 10 books from which he has to select 2 books

Q: 9 athletes are to take part in a race. In how many ways can the first 5 places be filled?

A: Given: 9 athletes are to take part in a race To find the number of ways the first 5 places are…

Q: a) From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at…

A: Given that from a group of 7 men and 6 women, five persons are to be selected to form a committee so…

Q: How many six-number combinations can be generated from the numbers from 1 to 42 inclusive, without…

A: Given information: A 6 number combination is to be generated. The possible numbers are selected…

Q: There are 10 students in a class. In how many ways can an instructor give exactly three students a…

A: Given that there are 10 students in a class. And exactly 3 students are given by a grade A.

Q: In how many ways can a chairperson and a vice chairperson be selected from a committee of 15 people?

A: For the following question

Q: in how many ways can a committee of 9 students be chosen from 8 juniors and 10 seniors if there must…

A: Given data: A committee of 9 students.

Q: In how many ways can 5 starting positions on a basketball team be filled with 8 men who can play any…

A: GivenNo.of Men(n)=8No.of positions(r)=5