Question

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? $\frac{1}{24}$ $\frac{1}{8}$ $\frac{1}{4}$ $\frac{1}{3}$

Explanation:

Step1: Calculate total number of sequences

We use the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$. Here $n = 4$ (red, yellow, blue, purple) 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 correctly on the first try is the reciprocal of the total number of possible sequences. So the probability $P=\frac{1}{24}$.

Answer:

$\frac{1}{24}$