There are 54 runners in a race. How many ways can the runners finish first, second, and third?
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- In a competition of 50 professional ballroom dancers, 22 compete in the fox-trot competition, 18 compete in the tango competition. and 6compete in both the fox-trot and tango competitions. How many dancers compete in the foxtrot or tango competitions?Alice and Bill have four grandchildren, and they have three framed pictures of each grandchild. They wish to choose one picture of each grandchild to display on the piano in their living room, arranged from oldest to youngest. In how many ways can they do this?Alice and Bill have four grandchild, and they have three framed pictures of each grandchild. They wish to choose one picture of each grandchild to display on the piano in their living room, arranged from oldest to youngest. In how many ways can they do this?
- In a group of 20 musicians, 12 play piano, 7 play trumpet, and 2 play both piano and trumpet. How many musicians play either piano or trumpet?Over the past year, John has purchased 30 books. In how many ways can he pick four of these books and arrange them, in order, on his nightstand bookshelf? In how many ways can he choose four of these books to take with him on his vacation at the shore?A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?
- A palette of water color paints has 3 shades of green, 3 shades of blue, 2 shades of red, 2 shades of yellow, and 1 shade of black. How many ways are there to choose one shade of each color?In three-card poker, a hand consists of three cards dealt from a deck of 52. How many different three-card poker hands are possible? (Order is not important.)There are 10 applicants for three sales positions at a department store. All of the applicants are qualified. In how many ways can the department store fill the three positions?
- Dance Committee A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 8 sophomores, 12 juniors, and 10 seniors are eligible to be on the committee, in how many ways can the committee be chosen?A coffee shop has 7 Guatemalan roasts, 4 Cuban roasts, and 10 Costa Rican roasts. How many ways can the shop choose 2 Guatemalan, 2 Cuban, and 3 Costa Rican roasts for a coffee tasting event?In how many ways can 10 teenagers be seated at a round table if 2 girls wish to sit with their boyfriends.
