How Many Ways Can 4 Different Prizes Be Given Away To 3 Boys GMAT Problem-Solving

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.

To determine the number of ways to distribute 4 different prizes among 3 boys, we can use the concept of permutations with repetition.

For each prize, there are 3 choices (boys) to whom it can be given. Since there are 4 prizes in total, we need to multiply these choices together to find the total number of possibilities.
3 choices for the first prize * 3 choices for the second prize * 3 choices for the third prize * 3 choices for the fourth prize = 3^4 = 81

Therefore, the correct answer is A. 81.

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.
We are given:

4 different prizes
3 boys who are eligible for all the prizes
To determine the number of ways to distribute these prizes, we can consider each prize individually.

For the first prize, there are 3 choices of boys who can receive it. Let's call these choices A, B, and C.
Now, for the second prize, we still have 3 choices of boys, namely A, B, and C. The same applies to the third and fourth prizes.
Since the prizes are given independently, we can multiply the number of choices for each prize together to get the total number of possibilities.

Number of choices for the first prize = 3 (A, B, or C)
Number of choices for the second prize = 3 (A, B, or C)
Number of choices for the third prize = 3 (A, B, or C)
Number of choices for the fourth prize = 3 (A, B, or C)

To find the total number of possibilities, we multiply these choices together:
3 choices for the first prize * 3 choices for the second prize * 3 choices for the third prize * 3 choices for the fourth prize = 3^4 = 81
Therefore, there are 81 different ways to distribute the 4 prizes among the 3 boys.

A is the correct answer.

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.

There are 3 boys and 4 prizes. Let's say we start by giving away the first prize. There are 3 boys who could win the first prize, so there are 3 ways to give away the first prize.

Once we've given away the first prize, there are 2 boys who could win the second prize. So there are 2 ways to give away the second prize.

We can continue in this way to give away the third and fourth prizes. At each step, there are one fewer boy who could win the prize, so the number of ways to give away the prize decreases by 1.
In the end, there are 3⋅2⋅1⋅1 = 3^4 = 81 ways to give away the 4 prizes.

The appropriate answer is A.