Factorials in Mathematics
This worksheet covers the concept of factorials, including calculation, properties, and applications in permutations and combinations, suitable for Grade 11 students.
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Factorials Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = .
2. The value of 0! is defined as .
3. Factorials are commonly used in probability and statistics, particularly in calculating the number of possible and combinations.
4. What is the value of 6!?
72
120
720
5040
5. Which of the following expressions is equivalent to n! / (n-2)!?
n
n(n-1)
(n-1)!
n!
6. Simplify the expression: 10! / (7! * 3!).
7. In how many distinct ways can the letters of the word 'MATH' be arranged?
8. The factorial function is defined for all real numbers.
True
False
9. If n > 1, then n! > (n-1)!.
True
False
10. A school club has 7 members. In how many ways can a president, vice-president, and secretary be chosen from the members?