How many ordered lists are there of seven items chosen from eight? ordered lists
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- How many ways can a baseball coach arrange the order of 9 batters if there are 15 players on the team?Choosing Officers From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer need to be filled. In how many different ways can the offices be filled?To allocate annual bonuses, a manager must choose his top four employees and rank them first to fourth. In how many ways can he create the ‘Top- Four” list out of the 32 employees?
- 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.)A buyer of a new sedan can custom order the car by choosing from 5 different exterior colors, 3 different interior colors, 2 sound systems, 3 motor designs, and either manual or automatic transmission. How many choices does the buyer have?How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?
- A coin club has five members. In how many different ways can there be a president and a vice-president?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?A motorcycle shop has 10 choppers, 6 bobbers, and 5 café racers—different types of vintage motorcycles. How many ways can the shop choose 3 choppers, 5 bobbers, and 2 café racers for a weekend showcase?
- How many unique ways can a string of Christmas lights be arranged from 9 red, 10 green, 6 white, and 12 gold color bulbs?Selecting surfboards In how many ways can 6 surfboards be selected from 24 different surfboards?How many distinguishable words can be formed from the letters of the word casserole if each letter is used exactly once?