There are 6 candidates running in a Presidential primary. After each primary, two of the candidates will withdraw, except for the last one, when the winner becomes the nominee. (a) The first primary has all 6 candidates. In how many ways could the 6 candidates finish the race? (b) The second primary will only have the top 4 finishers from the first race. How many ways could the 4 candidates finish the second race? (c) The third primary only has the 2 remaining candidates. How many ways could this race finish?

Q: 2-) In a factory there are (7) engineers and (5) accountants. A committee of (3) engineers and (2…

A: Given : In a factory, there are 7 engineers and 5 accountants. A committee of 3 engineers and 2…

Q: B-In a factory there are 5 engineers and 3 accountants. A committee of 2 engineers and 2 accountants…

A: Given,no.of engineers=5no.of accountants=3

Q: From a group of 9 men and 11 women, a committee consisting of 2 men and 2 women is to be formed. How…

A: Men=9Women=11Choose for a committee 2 men and 2 women

Q: A presidential candidate will be visiting 4 cities in Georgia, 2 cities in Mississippi, and 4 cities…

A: This is a counting problem, and we will solve this using the concept of permutations.

Q: A legislative committee consists of 8 Democrats and 10 Republicans. A delegation of 4 is to be…

A:

Q: At a movie​ festival, a team of judges is to pick the​ first, second, and third place winners from…

A: It is given that there are totally 19 films entered at a movie festival.

Q: Soccer Shootout In soccer, a tie at the end of regulation time leads to a shootout by three members…

A: From the provided information, the total number of players are 11.The required total number of ways…

Q: quarters, and you select 3 coins:   (d) In how many ways can the selection be made if you have…

A: Given that there are  8 dimes and 4 quarters Suppose three coins are selected . (d) The objective is…

Q: A class consists of 10 boys and 15 girls. They want to elect officers so that the president and…

A: (a) Find the number of possible ways to elect 4 officers out of 10 boys and 15 girls. (b) Find the…

Q: rst prize is one million dollars, the second prize is one hundred thousand dollars, and the third…

A: Permutation and combination When a letter, people. etc. are to be arranged in such a way that the…

Q: are possible? (a) How many different delegations The 4 delegates can be selected different ways. (b)…

A: Solution: The total number of delegates to be chosen is 4. The number of available resources to…

Q: How many different ways can the golf pro at a golf club select a foursome consisting of 1 man and 3…

A: Given,   Number of males = 8 Number of females = 11   The objective is to find how many different…

Q: 10 people is choosing a chairperson and vice chairperson

A: Given that   A group of 10 people = (n)=10 We have to select two people from total 10 people.…

Q: A group of 10 people in s choosing a Chairperson and Vice President. They put all 10 people's names…

A:

Q: three lotter tickets for first, second and third prizes are drawn from a group of 40 tickets. find…

A: given data select first, second and third prizes from a group of 40 tickets.

Q: A class is holding elections for class president, vice president, and secretary. There are 18…

A: A class is holding elections for class president, vice president, and secretary. There are 18…

Q: An engineer is putting together a train with 5 box cars, 3 tank cars, and 4 flat cars. For the box…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

Q: On a ballot, the candidates for each office are listed together under the office for which they are…

A: Here the given information is  On a ballot, the candidates for each office are listed together under…

Q: (a) married to each other and (b) not married to each other

A: Since , there are 15 married couples in a room Our aim is to determine the number of possible ways…

Q: marching band consists of 11 pipers and 12 drummers.  Three of them are selected to march in order…

A: The formula for Permutation is nPr = n!/(n – r)!. Explanation: Consider that r items need to be…

Q: A team of 6 people is to be chosen from a group of 7 girls and 4 boys. There ae possible teams if…

A: Combination formula :  Number of ways to select  r items from total n items is given by,   Crn =…

Q: A class has 30 students. For a school event, 15 students need to be chosen from this class. 5 of the…

A:

Q: . How many different ways are there of handing out the prizes if (a) the prizes are all the same?…

A: A kindergarten class has 18 children. FIve of the children are selected to receive prizes. Here use…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.