A raffle contains 150 tickets there are 3 prizes assuming all tickets were sold how many different ways can prizes be awarded if

A. One ticket can win more than one prize
B. One ticket can only win one prize

A. 150^3

B. 150 * 149 * 148

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To solve this problem, we can use the concept of permutations. Permutations are used to calculate the number of ways a group of items can be arranged when the order matters. In this case, we need to consider two scenarios: one where one ticket can win more than one prize (part A), and another where one ticket can only win one prize (part B).

A. One ticket can win more than one prize:
In this scenario, we have three prizes and each ticket can win any number of prizes (even all three). It can be solved by finding all possible combinations of prizes won by each ticket independently.

To calculate the number of ways, we can use the formula for the total number of combinations. For each prize, we have 2 choices: either the ticket wins it or it doesn't. Therefore, the total number of combinations would be 2 raised to the power of the number of prizes.

In this case, with 3 prizes, there are 2^3 = 8 different ways to award the prizes if one ticket can win more than one prize.

B. One ticket can only win one prize:
In this scenario, each ticket can only win one prize. This is similar to finding the number of permutations.

To calculate the number of ways, we can use the formula for the total number of permutations. Starting with the first prize, there are 150 possible tickets that can win it. For the second prize, since one ticket has already won a prize, there are 149 tickets left. Similarly, for the third prize, there are 148 tickets remaining.

Using the formula for permutations, we multiply the choices for each prize together: 150 * 149 * 148.

Thus, if one ticket can only win one prize, there are 150 * 149 * 148 = 3,324,600 different ways to award the prizes.

In summary:
A. One ticket can win more than one prize: 8 different ways
B. One ticket can only win one prize: 3,324,600 different ways.