Question:medium
The 10 letters of the word STATISTICS are arranged randomly. The probability that the 10-letter arrangement starts with CAT is
The 10 letters of the word STATISTICS are arranged randomly. The probability that the 10-letter arrangement starts with CAT is
Show Hint
To simplify probability calculations with factorials, always cancel the common terms (like \(7!\) and \(3!\)) before multiplying out large numbers. It reduces the chance of arithmetic error.
Updated On: Jun 24, 2026
- \(\frac{1}{80}\)
- \(\frac{1}{120}\)
- \(\frac{1}{240}\)
- \(\frac{1}{280}\)
- \(\frac{1}{360}\)
Show Solution
The Correct Option is C
Solution and Explanation
Was this answer helpful?
0
Top Questions on Probability
- The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]- MHT CET - 2024
- Mathematics
- Probability
- If \( X \) is a random variable with the probability mass function (p.m.f.) as follows: \[ P(X = x) = \begin{cases} \frac{5}{16}, & x = 0, \\ \frac{kx}{48}, & x = 1, \\ \frac{1}{4}, & x = 2, \\ \frac{1}{4}, & x = 3, \end{cases} \] then find \( E(X) \):
- MHT CET - 2024
- Mathematics
- Probability
- The p.m.f. of a random variable \( X \) is: \[ P(X) = \frac{2x}{n(n+1)}, \quad x = 1, 2, 3, \ldots, n \] \[ P(X) = 0, \quad \text{Otherwise.} \] Then \( E(X) \) is:
- MHT CET - 2024
- Mathematics
- Probability
- Find the expected value and variance of \( X \) for the following p.m.f: \[ \begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline P(X) & 0.2 & 0.3 & 0.1 & 0.15 & 0.25 \\ \hline \end{array} \]
- MHT CET - 2024
- Mathematics
- Probability
- Want to practice more? Try solving extra ecology questions todayView All Questions
