Question

determine whether the object is a permutation or a combination.
a hand of cards in poker

choose the correct answer below.
a. this is a permutation because repetition is not allowed and the order of the items matters.
b. this is a combination because repetition is not allowed and the order of the items does not matter.
c. this is neither a permutation nor a combination because repetition is allowed.
d. there is not enough information given to make a decision.

Explanation:

To determine if a poker hand is a permutation or combination, we analyze:

• In poker, a hand consists of 5 cards. Repetition (drawing the same card more than once) is not allowed.
• The order of cards in a hand does not matter (e.g., a hand with Ace - King - Queen is the same as King - Ace - Queen in terms of the hand’s value).
• A combination is defined as a selection of items where order does not matter and repetition is not allowed, while a permutation requires order to matter. So a poker hand fits the definition of a combination.

Answer:

B. This is a combination because repetition is not allowed and the order of the items does not matter.