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"Determine the value of each of the following:
b. 0!"
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4. Probability
Counting
Scelta multipla
You want to arrange the books on your bookshelf by color. How many different ways could you arrange 12 books if 4 of them have a blue cover, 3 are yellow, and 5 are white?
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B
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Identify the total number of books to arrange, which is 12.
Recognize that the books are grouped by color: 4 blue, 3 yellow, and 5 white.
Use the formula for permutations of multiset: \( \frac{n!}{n_1! \times n_2! \times n_3!} \), where \( n \) is the total number of items, and \( n_1, n_2, n_3 \) are the counts of each distinct item.
Substitute the values into the formula: \( \frac{12!}{4! \times 3! \times 5!} \).
Calculate the factorials: \( 12! \), \( 4! \), \( 3! \), and \( 5! \), and then divide as per the formula to find the number of arrangements.
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