Question Detail

STA 112 PERMUTATIONS AND COMBINATIONS Objective Question

Question

Which of the following statements is TRUE?
Options
A 0! = 0
B n! / (n-r)! = n
C nPn = 1
D nCr = nCn-r
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

Let's evaluate each option:(A) 0! = 0: This is False. By definition, 0! = 1.(B) n! / (n-r)! = n: This is False. n! / (n-r)! is the definition of nPr. For example, 3P2 = 3!/(3-2)! = 6, which is not equal to n=3.(C) nPn = 1: This is False. nPn = n! / (n-n)! = n! / 0! = n! / 1 = n!. For example, 2P2 = 2! = 2, which is not 1.(D) nCr = nCn-r: This is True. This is a fundamental property of combinations, often called the symmetry property. For example, 5C2 = 10 and 5C(5-2) = 5C3 = 10.

Hint

Recall the definitions and fundamental properties of factorials, permutations (nPr, nPn), and combinations (nCr).

Question Info