Question

A jar contains 14 marbles, out of which 5 are white, 5 are blue, and 4 are green. If 3 marbles are drawn without replacement, what is the probability that the marbles do not change their original positions?

Hint:

For probability questions: \begin{itemize} \item Total outcomes = total possible combinations, \item Favourable outcomes depend on the condition given, \item Probability = $\dfrac{\text{Favourable}}{\text{Total}}$. \end{itemize}

Answer 1

Step 1: Total number of marbles in the jar \(=14\).
Step 2: Number of ways to choose any 3 marbles from 14 is: \[ ^{14}C_3 = 364 \]
Step 3: Only one favourable outcome exists where the selected marbles remain in their original positions.
Step 4: Therefore, the probability is: \[ \text{Probability} = \frac{1}{364} \]