FTCE Professional Education Practice Exam

Disable ads (and more) with a membership for a one time $2.99 payment

Prepare for the FTCE Professional Education Test. Study with comprehensive flashcards and engaging multiple choice questions, each crafted with hints and detailed explanations. Enhance your confidence for success!

Each practice test/flash card set has 50 randomly selected questions from a bank of over 500. You'll get a new set of questions each time!

Practice this question and more.

What is the equation used to calculate combinations?

n!(n-r)!/r!
n!/(n-r)!r!
n!/r!(n-r)!
nCr = n!/(n-r)

The correct answer is: n!/r!(n-r)!

The equation used to calculate combinations is represented as n! / (r!(n - r)!), which reflects a fundamental concept in combinatorics. This formula is used to determine the number of ways to choose r items from a total of n items where the order of selection does not matter. In this equation, n represents the total number of items, r represents the number of items being chosen, n! (n factorial) represents the product of all positive integers up to n, and r! and (n - r)! account for the internal arrangements of the chosen and unchosen items, respectively. By dividing n! by r!(n - r)!, the formula effectively removes the arrangements of chosen items (since the order does not matter) and the arrangements of the remaining items. This results in a count of distinct combinations possible from the larger set. The rationale behind the other options lies in their structure, reflecting errors either in the arrangement of the factorial terms or in the omission of necessary components for accurately calculating combinations. Therefore, the recognized formula for combinations encapsulates essential combinatorial principles, illustrating how selections can be made without concern for order.