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

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

Answer

Explanation:

Step1: Calculate total number of sequences

We use permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 4$ (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

There is only 1 correct sequence. Probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{1}{24}$.

Answer:

$\frac{1}{24}$