Problem

A lottery exists where palls numbered 1 to 19 are placed in an urn. To win, you must match the four balls chosen in the correct order. How many possible outcomes are there for this game?
The number of possible outcomes is (Simplify your answer.)

Answer

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Answer

Final Answer: The number of possible outcomes is \(\boxed{93024}\).

Steps

Step 1 :A lottery exists where balls numbered 1 to 19 are placed in an urn. To win, you must match the four balls chosen in the correct order. We need to find out how many possible outcomes are there for this game.

Step 2 :This is a permutation problem because the order of the numbers matters. We are choosing 4 balls out of 19.

Step 3 :The formula for permutations is: \(P(n, r) = \frac{n!}{(n-r)!}\) where n is the total number of items, r is the number of items to choose, and "!" denotes factorial, which is the product of all positive integers up to that number.

Step 4 :In this case, n = 19 and r = 4, so we need to calculate \(P(19, 4)\).

Step 5 :By substituting the values into the formula, we get \(P(19, 4) = \frac{19!}{(19-4)!}\).

Step 6 :After calculating, we find that there are 93024 possible outcomes for this lottery game.

Step 7 :Final Answer: The number of possible outcomes is \(\boxed{93024}\).

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