A married couple decides to have a party. The husband has 8 friends and the wife has 9 friends. Unfortunately, none of the husband’s friends will attend a party that is attended by any of his wife’s friends. How many different parties of size 4 can the couple have?

Q: A bag contains 3 lemon, 2 cherry, and 6 grape candies. A handful of 4 candies is grabbed from the…

A: At most 1 grape candy means 0 or 1 grape candy. There are 6 grape candies and (3+2)=5 non-grape…

Q: A group of 12 people are going to run a race. The top 6 finishers are going to advance to the next…

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Q: At one family reunion, every niece was a cousin. Half of all aunts were cousins. Half of all cousins…

A:

Q: there are 6 men and 7 women in the math club. a committee is to be formed consisting of 3 men and 4…

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Q: A class has 32 students.  18 have hats, and 17 do not wear glasses.  5 students wear glasses but do…

A: We use ven diagram to solve this problem.

Q: Of 20 possible books, you plan to take 9 with you on vacation. How many different collections of 9…

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Q: A basketball team contains 21 players. If 5 people can be on the court at one time, how many…

A: Given that Number of players (n)=21  Number of people on the court at one time  r=5  We have to find…

Q: In a local recreational soccer league there are 60 men and 252 women signed up to play. The…

A: We need to equally divide men and women and then find when number of team formed from both sides are…

Q: The Diaz family is selecting a furniture set. A furniture set has a bed, a desk and a dresser. There…

A: The objective of this question is to find out the total number of different furniture sets the Diaz…

Q: You are forming an 9-member swim team from 13 girls and 16 boys. The team must consist of five boys…

A: We have given that that 9-member swim team from 13 girls and 16 boys  The team must consist of five…

Q: In a group of 100 people, 60 have a DVD player, 50 have a CD player, and 20 have neither. How many…

A:

Q: Of 13 possible​ books, you plan to take 4 with you on vacation. How many different collections of 4…

A: The objective of this question is to find out the number of different collections of 4 books that…

Q: The Hickory Stick has a selection of 4 meats and 7 vegetables. How many different selections of one…

A:

Q: There are 10 students that are a part of a chess club. 2 kids can play a game of chess at once. How…

A: Ans -:  There are 10 students that are a part of a chess club. 2 kids can play a game of chess at…

Q: At a race track you have the opportunity to buy a ticket that requires you to pick the first and…

A:

Q: the track team has 20 members and will be sending 5 members to the next competition. how many 5…

A: Combinations: The number of combinations of r items selected from n items is, nr=n!n-r!r! The track…

Q: The Wycoffs are planning their next family night. They always have dinner out somewhere and then do…

A: The answer is attached below,

Q: A doctor visits her patients during morning rounds. In how many ways can the doctor visit 7 patients…

A: Given Number of patients=7

Q: Charmaine asked 8 students how many courses they have taking so far at her college. Here is the list…

A: Solution: The given data is 13, 20, 8, 17, 22, 4, 15 and 18.

Q: A clown owns 8 hat(s), 7 horn(s), 6 oufits. How many different outfits can the clown put together if…

A: Solution

Q: A child has fewer than 300 baseball cards. If he puts them in piles of 3​, 4​, 6​, 15​, or 18 he has…

A: Let, the child has x baseball cards.  Then, according to the given problem,        x = 1 (mod 3)…

Q: Joey finds 13 video games that he would like to have. Three of them will run on his operating system…

A: Given: A total of 13 games are there. 10 will run on the operating system and 3 will not.

Q: At a race track you have the opportunity to buy a ticket that requires you to pick the first and…

A: pick the first and second places in the firdt two races.  first race runs 12 horses second race runs…

Q: A class has 13 ​students, of which 4 are seniors. How many committees of size 4 can be selected if…

A: Combination of n objects taken r at a time = n!(n-r)!r! where 0≤r≤n.

Q: There are 24 students playing basketball at lunch. How many different three-person teams can be…

A:

Q: How many different 6 card hands can be dealt from a deck of 52 cards? The order of the cards does…

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

Q: The manager of the winning soccer team chooses three of the 20 members to be interviewed by a sports…

A:

Q: A poker hand consists of five cards from a deck of 52.  Order does not matter.  In how many ways can…

A: A poker hand consists of five cards from a deck of 52.   Order does not matter i.e. combination is…

Q: Suppose you have a choice of ten TV sets that can be matched with any of six DVR players and eight…

A: Multiplication rule of counting: If a task consists of a sequence of choices in which there are ‘a’…

Q: A party room has a circular table with 12 seats. A group of 4 people enter the room. How many…

A: In a circular table with n seats,  there are (n-1)! ways ofoccupying the seats