Questions: What is meant by the term "combination"? What is the difference between a permutation and a combination? A combination is a selection of objects. In a combination, as opposed to a permutation, order (Choose one) matters does not matter

Solution Steps

A combination is a selection of items from a larger pool where the order of selection does not matter. In contrast, a permutation is a selection where the order does matter. To calculate combinations, we use the formula for combinations, which is C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from, and k is the number of items to choose.

A combination is defined as a selection of items from a larger set where the order of selection does not matter. The mathematical expression for combinations is given by:

\[ C(n, k) = \frac{n!}{k!(n-k)!} \]

where \( n \) is the total number of items, and \( k \) is the number of items to choose.

In this case, we have \( n = 5 \) and \( k = 3 \). We can substitute these values into the combination formula:

\[ C(5, 3) = \frac{5!}{3!(5-3)!} = \frac{5!}{3! \cdot 2!} \]

Calculating the factorials, we find:

\[ 5! = 120, \quad 3! = 6, \quad 2! = 2 \]

Thus, we can compute:

\[ C(5, 3) = \frac{120}{6 \cdot 2} = \frac{120}{12} = 10 \]

The number of combinations of choosing 3 items from a set of 5 is \( 10 \).

Final Answer