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Permutations and Combinations

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How many unique ways can 5 different books be arranged on a shelf?

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120 ways

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How many different ways can a 7-member delegation be arranged in a single file for a photo?

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5,040 ways

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How many combinations of toppings can be chosen for a pizza if there are 7 toppings available and you can choose up to 3?

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64 combinations

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If there are 8 runners in a race, how many ways can the gold, silver, and bronze medals be awarded?

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336 ways

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How many anagrams can be formed from the letters of the word 'BANANA'?

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60 anagrams

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How many 3-digit numbers can be made using the digits 1, 2, 3, 4, 5, if no repetition is allowed?

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60 numbers

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How many different 4-digit PIN codes can be created using the numbers 0 through 9 if numbers can be repeated?

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10,000 PIN codes

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How many 2-letter words can be formed with the letters A, B, C, with repetition allowed?

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9 words

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How many distinct ways can the letters of the word 'LEVEL' be arranged?

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60 ways

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How many ways can a photographer arrange 10 models in 5 different poses?

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30,240 ways

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How many unique sets of 3 colors can be made from 5 different colors?

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10 sets

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How many ways can a committee of 4 be formed from a pool of 12 candidates?

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495 ways

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How many ways can you arrange 6 out of 9 books on a shelf?

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60,480 ways

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In how many ways can a president, vice-president, and treasurer be chosen from a group of 10 people?

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720 ways

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How many ways can 8 people be seated in a row of 8 seats at the cinema?

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40,320 ways

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How many different signals can be made by arranging 3 flags in order from a set of 6 different flags?

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120 signals

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How many ways can a teacher assign 5 different books to 5 students if every student must receive exactly one book?

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120 ways

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How many possible four-character license plates can be made if the first two characters must be letters and the last two must be numbers, with repetition allowed?

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67600 plates

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How many different ways can you choose a group of 3 starters from a basketball team of 10 players?

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120 ways

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In a standard deck of 52 cards, how many ways can you draw a hand of 5 cards?

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2,598,960 ways

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