Question

In a guessing game where one player places four different-colored pegs in positions a, b, c, or d, and a second player tries to guess the configuration, how many possibilities exist for the second player to guess correctly if repetition of colors is allowed?

a) 256
b) 64
c) 81
d) 24

Answer 1

The number of possible configurations in the guessing game is the number of colors raised to the power of the number of positions.

Step-by-step explanation:

The game described in the question is similar to Mastermind or any other code-breaking game where repetition of colors is allowed. To find the total number of possibilities that the second player has to guess correctly, we use the concept of permutations with repetition. Since there are four positions each can be occupied by any one of the available colors, the number of possibilities is equal to the number of unique colors raised to the power of the number of positions.

For instance, if there are n different colors, the number of possible configurations for four positions is n4. As it is not specified how many different colors there are.

If we assume the typical Mastermind game with 6 different colors, then the total number of possibilities would be 64 = 1296, which is not listed in the given options.

The material provided seems unrelated to the student's original question, as it discusses probabilities with marbles and kittens, which does not pertain to the guessing game with colored pegs.