Virtual Labs

1. What is the value of 6! (6 factorial)?

a: 720 Explanation

Explanation

b: 120 Explanation

Explanation

c: 5040 Explanation

Explanation

d: 36 Explanation

Explanation

2. Which of the following is NOT a property of factorials?

a: 0! = 1 Explanation

Explanation

b: n! is always positive for n ≥ 0 Explanation

Explanation

c: n! is the sum of all numbers from 1 to n Explanation

Explanation

d: n! is used in permutations and combinations Explanation

Explanation

3. What is the number of trailing zeroes in 100!?

a: 24 Explanation

Explanation

b: 20 Explanation

Explanation

c: 10 Explanation

Explanation

d: 5 Explanation

Explanation

4. Which formula gives the number of digits in n! ?

a: n Explanation

Explanation

b: n^2 Explanation

Explanation

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

Explanation

d: n! / 10 Explanation

Explanation

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

a: 40320 Explanation

Explanation

b: 5040 Explanation

Explanation

c: 720 Explanation

Explanation

d: 362880 Explanation

Explanation

6. What is the main reason for using logarithms to compute the number of digits in n! ?

a: Logarithms are faster to compute than multiplication for large n Explanation

Explanation

b: Logarithms always give exact values Explanation

Explanation

c: Multiplication is not allowed in programming Explanation

Explanation

d: Logarithms are only used for small n Explanation

Explanation

7. In how many ways can 5 students be arranged in a line?

a: 120 Explanation

Explanation

b: 60 Explanation

Explanation

c: 24 Explanation

Explanation

d: 720 Explanation

Explanation

8. Which of the following statements about trailing zeroes in n! is true?

a: They are caused by pairs of 2 and 5 in the factorization of n! Explanation

Explanation

b: They are caused by pairs of 3 and 7 Explanation

Explanation

c: They are caused by the number of digits in n! Explanation

Explanation

d: They are caused by the value of n Explanation

Explanation

9. Which of the following is NOT a use of factorials?

a: Counting arrangements (permutations) Explanation

Explanation

b: Calculating binomial coefficients Explanation

Explanation

c: Finding the sum of a geometric series Explanation

Explanation

d: Taylor series expansions Explanation

Explanation

10. What is the value of 0! ?

a: 0 Explanation

Explanation

b: 1 Explanation

Explanation

c: Undefined Explanation

Explanation

d: Depends on n Explanation

Explanation

Factorials