How many different 4 card hands can be drawn from a set of 30 cards

if:

Step-by-step explanation:

.

Assume for now that the ordering of the four cards does matter. Hands like and would then be considered different from one another.

There would choices for the first card. Since the first card was not returned to the pile, there would be only choices for the second card. Likewise, there would be choices for the third card and for the fourth.

By this reasoning, there would be different ways to draw a hand of four cards from this set when the ordering of these four cards do matter.

However, in many card games, once a hand of cards is drawn, the ordering of cards within that hand does not matter. In other words, hands like and would not be considered as distinct from one another.

In that case, the ways of drawing cards would include a large number of duplicates.

There are be ways to arrange a hand of four cards when the order matter. Hence, when the ordering within a hand no longer matters, each hand of four cards would have been counted times among those ways.

Therefore, when the ordering of cards within a set does not matter, would give the number of distinct ways to draw a hand of four out of this set of thirty distinct cards.

it is 570

step-by-step explanation: