A class contains 9 boys and 3 girls. (a) In how many ways can the teacher choose a committee of 4? (b) How many of them will contain atleast one girl? (c) How many of them will contain exactly one girl?

Q: Ten pirates find a sack of gold coins. When they try to divide up the gold (with equal shares for…

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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: This year, there are ten freshmen, eight sophomores, nine juniors, and nine seniors are eligible to…

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Q: The math club at college has 16 students - 10 males and 6 females. (a) The club wants to select a…

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Q: A boy owns 6 pairs of pants, 9 shirts, 10 ties, and 4 jackets. (a) How many outfits can he wear to…

A: Given data:     The given pairs of pants are: P=6. The given number s of shirts are: S=9. The given…

Q: Committee: The Student Council at a certain school has seven members. Four members will form an…

A: Given,Total no.of members=7

Q: A volleyball team has ten players. To play a game, 6 players are needed to play positions numbered…

A: No. of players in the volleyball teamNo. of players needed to playThe positions are numbered from…

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: 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: Student Painters, which specializes in painting the exterior of residential buildings, has nine…

A: The number of ways r items can be selected from n different items is equal to C(n,r) . The formula…

Q: A group of Mathematics faculty at the local college consists of 10 women and 10 men. Five people are…

A: Given  No of men = 10 No of women = 10 We need to select 5 people

Q: Apolice department in a small city consists of 10 officers. If the department policy is to have 5 of…

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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: A boy owns 10 pairs of pants, 6 shirts, 2 ties, and 9 jackets. (a) How many outfits can he wear to…

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

Q: You are teaching a math class, and have seventeen students who are so hard-working and invested, you…

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

Q: Suppose we want to choose 2 objects, without replacement, from the 3 objects pencil, eraser, and…

A: Let,P= pencil E= eraser D= deskHere we are using the formulae for permutation and combinations.

Q: How many different committees of 3 people can be formed from a pool of 7 people? A We need to pick a…

A: Given: There is a pool of 7 people.

Q: If Joe only has room for 2 of his 6 flags on his flagpole, how many different ways can they be…

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Q: s can this be done, if the order of the choices is taken into s can this be done, if the order of…

A: Given Suppose we want to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.

Q: In how many ways can a subcommittee of eight be chosen from a Senate committee of seven Democrats…

A: We have to find In how many ways can a subcommittee of eight be chosen from a Senate committee of…