Virtual Labs

1. What is the value of 4! (4 factorial)?

a: 10 Explanation

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b: 24 Explanation

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c: 16 Explanation

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d: 12 Explanation

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2. Which of the following best describes n! (n factorial)?

a: The sum of all numbers from 1 to n Explanation

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b: The product of all numbers from 1 to n Explanation

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c: The product of all even numbers up to n Explanation

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d: The sum of all even numbers up to n Explanation

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3. What is the value of 0! (zero factorial)?

a: 0 Explanation

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b: 1 Explanation

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c: Undefined Explanation

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d: Depends on n Explanation

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4. Which of the following grows fastest as n increases?

a: n Explanation

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b: n^2 Explanation

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c: n! Explanation

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d: 2n Explanation

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5. What is the main reason why direct computation of large factorials is difficult on a computer?

a: Factorials can be negative Explanation

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b: Factorials grow very quickly and exceed standard data types Explanation

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c: Factorials are always prime Explanation

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d: Computers cannot multiply Explanation

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6. Which formula can be used to find the number of digits in n! without computing n! directly?

a: n Explanation

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b: n^2 Explanation

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c: floor(log10(n!)) + 1 Explanation

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d: n! / 10 Explanation

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7. How do you count the number of trailing zeroes in n!?

a: Count the number of times n is divisible by 2 Explanation

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b: Count the number of times n is divisible by 5 Explanation

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c: Count the number of pairs of 2 and 5 in the factorization of n! Explanation

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d: Count the number of digits in n! Explanation

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8. Which of the following is the value of 5! ?

a: 120 Explanation

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b: 60 Explanation

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c: 24 Explanation

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d: 720 Explanation

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9. Which of the following statements about factorials is false?

a: 0! = 1 Explanation

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b: n! is always even for n > 2 Explanation

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c: n! is the product of all positive integers up to n Explanation

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d: n! is always a prime number Explanation

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10. In how many ways can 3 books be arranged on a shelf?

a: 3 Explanation

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b: 6 Explanation

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c: 9 Explanation

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d: 12 Explanation

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