Question

The number of possible combinations if r objects are taken from n items is ₙCᵣ =____________A. n!/r! B. n!/(n - r)! C. n! D. n!/(n - r)! r!.

Answer 1

The number of possible combinations if r objects are taken from n items is n!/r!(n-r)!. This is option D in the given choices.

Step-by-step explanation:

The number of possible combinations if r objects are taken from n items is nCr = n!/(r!(n-r)!). This is option D in the given choices. It represents the number of ways to select r objects out of n items, taking into account that the order doesn't matter. To calculate this, we use the formula for combinations, which is n factorial divided by the factorial of r multiplied by the factorial of (n-r). For example, if we want to choose 3 objects out of 5, the formula would be 5!/(3!(5-3)!), which simplifies to 5!/(3!2!).