Suppose that 9 horses run a race. How many first-, second-, and third-place finishes are possible?

Q: calculate the number of ways that the first, second, and third place horses can finish in a race…

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Q: Two coins are randomly drawn from a coin pouch. If there are 5 dimes, 2 nickels, and a quarter, how…

A: As given there are 5 dimes, 2 nickels, and a quarter in a pouch. 1 nickel = 5 cents 1 dime = 10…

Q: Thirteen people are entered in a race. If there are no ties, in how many ways can the first three…

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Q: Two coins are randomly drawn from a coin pouch. If there are 4 dimes, 2 nickels, and a quarter, how…

A: The pouch contains 4 dimes, 2 nickels and one quarter. Two coins are randomly drawn from a pouch.

Q: In how many ways can you 9 players be choosen from a team with 14 members?

A: Given:Total number of members in the team, n = 14.Number of players to be selected, r = 9.

Q: Two coins are randomly drawn from a coin pouch. If there are 4 dimes, 3 nickels, and a quarter, how…

A: The probability density function of X is obtained below:From the given information, number of coins…

Q: In a horse race, how many different finishes among the first 3 places are possible if 12 horses are…

A: Finishes  among the first  3 places  are possibleif  12  horses  are running

Q: Suppose 15 cars start at a car race. In how many ways can the top 3 cars finish the​ race? The…

A: Permutations: The number of permutations of r items selected from n items is, Prn=n!n-r! In this…

Q: Suppose there is a club of 15 people. In how many ways can a committee of 3 people be selected?

A: Our objective is to find the number of way

Q: A race has 10 runners. In how many ways can the first three places be decided?

A: Here use combination

Q: A store sells 8 kinds of balloons with at least 30 of each kind. How many different combinations of…

A: 8 kinds of balloons with at least 30 of each kind We have to find how many different combinations of…

Q: Twelve people compete in a downhill ski race. Assuming that there are no ties, in how many different…

A: Solution: If there are n objects and are arranged with the order r, then the permutation should be…

Q: A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the…

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Q: At the horse races (with ten horses competing), in how many ways can the top three places be…

A: Permutation: The number of different arrangements of ‘r’ elements from a set of‘n’ elements is…

Q: The number of permutation of n items is also called as _______________.

A: We have to fill the blank with the correct information -  The number of permutation of n items is…

Q: Out of 9 children, in how many ways can a family have at least 1 girl?

A: We have given that, 9 children i.e. n=9 and family have at least 1 girl i.e. r=1   Combination…

Q: How many different ways can a race with 6 runners be completed? (Assume there is no tie.)

A: Given that number of runners is 6 The place that race completion has=6 places Since, from 1st place…

Q: In how many ways can eight children posing for a photograph line up in a row?

A: 8! = 40320 ways can eight children posing for a photograph line up in a row

Q: Suppose a class has 18 women and 12 men.We wish to form a committee of 5 people.If the committee is…

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Q: In a lottery, six numbers are randomly chosen from the set {1, 2, 3, ... 49}, so there are possible…

A: Hint: It is given that there are 1,2,...49 numbers. We are choosing 6 numbers from it. Now, obtain…

Q: How many ways are there to pair 2n people?

A: We need to compute the number of ways in which 2n people can be paired.

Q: Ten jokes are listed in a magazine.   If the fourth joke from the magazine is​ excluded, in how…

A: There are 10 jokes listed in a magazine.Here 4th joke is excluded than find the number of ways…

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: In how many ways can a group of 6 students be selected from 7 students?

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Q: There are 10 people in a meeting. In how many ways can you arrange your participants around a ROUND…

A: Total ways in which 10 people be arranged around a round table so that 4 people sit beside each…

Q: Certain automobile license plates consist of a sequence of three letters followed by four digits. If…

A: We have a license plate that consists of a sequence of three letters followed by four digits. The…

Q: Six players are to be selected from an 11​-player baseball team to visit schools to support a summer…

A: No. Of total students = 11 No. Of player to select = 6.

Q: Suppose 58 cars start at a car race. In how many ways can the top 3 cars finish the​ race?

A: We have to find no of  ways can the top 3 cars finish the​ race...

Q: How many possible ways can the top 5 finishers come in during a race with 24 racers? Each place…

A: This is a permutation problem.   Out of the 24, there will be 5 racers in the top 5.

Q: How many different ways can a race with 8 runners be completed? (Assume there is no tie)

A: There are 8 runners in the race and there is no tie. If two events E1 and E2 occur in order and E1…

Q: There are 6 runners in a race. In how many ways can 3 runners finish in first, second, and third to…

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Q: A committee of 8 people randomly chooses 3 people in order to be president, vice president, and…

A: Total person = 8 to chosen = 3 Order = considered

Q: In how many ways can 5 sets of numbers be picked from 50 numbers in a lottery?

A: From the provided information, Total numbers in a lottery = 50 The required number of ways of…

Q: An election ballot asks voters to select 2 city commissioners from a group of 6 candidates. In how…

A: An election ballot asks voters to select 2 city commissioners from a group of 6 candidates. I Total…

Q: (b) From a collection of 52 store customers, 3 are to be chosen to receive a special gift. How many…

A: a group of 52 store customers. 3 persons are to be selected, need to find total way exactly 3 store…

Q: In how many ways can a person choose three movies to watch from a collection of 7 suggested movies?

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

Q: The number of permutations of n items is also called as _______________.

A: The number of permutations of n items is also called as n! (n Factorial).

Q: The “Top Three” at a racetrack consists of picking the correct order of the first three horses in a…

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Q: 78% of households have a computer (laptop or desktop) and 75% have a hand-held device (tablet or…

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Q: There are 10 defective light bulbs in a bin containing 25 light bulbs. In how many ways can you…

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Q: In how many ways can a couple invite 3 out of their 15 closest friends to a dinner party?

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Q: How many different ways can a race with 9 runners be completed? (Assume there is no tie.)

A: There are 9 runners who can come in first so there are 9 possibilities  For the second place there…

Q: how many pairs (two cards with the same face and three cards with all different faces) are possible…

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Q: there are 15 horses in a race, how many possibilities are there for the win, place, and show (first,…

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Q: Suppose there are 14 people from which you can choose a President, Vice President, and a Treasurer.…

A: The number of people is 14.

Q: Three members of a committee will be randomly selected from five people. How many different…

A: We have to find number of different combinations possible.

Q: A bus has 8 vacant seats in the first rows. If 3 additional passengers enter the bus, in how many…

A: For the number of ways of their seating, we need to use combination.

Q: How many different ways a president and a vice president  can be selected from a group of 14…

A: To find the number of different ways in which a president and a vice president can be selected from…

Q: How many different ways can a race with 7 runners be completed? (Assume there is no tie.)

A: The number of runners in the race is 7. Assume that there is no tie. Then, the 7 runners will finish…

Q: How many combinations are possible to select a student president, vice president and treasurer among…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.