two children are playing a code - breaking game. one child makes a sequence of three colors from red…

two children are playing a code - breaking game. one child makes a sequence of three colors from red, yellow, blue, and purple. the other child must guess the sequence of colors in the correct order. once one color is used, it cannot be repeated in the sequence. what is the probability that the sequence is guessed on the first try? 1/24 1/8 1/4 1/3

two children are playing a code - breaking game. one child makes a sequence of three colors from red, yellow, blue, and purple. the other child must guess the sequence of colors in the correct order. once one color is used, it cannot be repeated in the sequence. what is the probability that the sequence is guessed on the first try? 1/24 1/8 1/4 1/3

Answer

Answer:

A. $\frac{1}{24}$

Explanation:

Step1: Calculate number of permutations

The number of permutations of 4 colors taken 3 at a time is given by the formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 4$ and $r=3$. So $P(4,3)=\frac{4!}{(4 - 3)!}=\frac{4!}{1!}=4\times3\times2=24$.

Step2: Determine probability

The probability of guessing the correct sequence on the first try is $\frac{1}{\text{total number of possible sequences}}$. Since there are 24 possible sequences, the probability is $\frac{1}{24}$.