Question:medium
A committee of 4 people is selected from the members of a school council which consists of 5 students, 4 teachers and 3 administrators. The probability that the committee has no teachers is
A committee of 4 people is selected from the members of a school council which consists of 5 students, 4 teachers and 3 administrators. The probability that the committee has no teachers is
Show Hint
Instead of calculating factorials fully, simplify the fractions in combination notation. For example, \(\frac{8 \cdot 7 \cdot 6 \cdot 5}{12 \cdot 11 \cdot 10 \cdot 9}\) allows you to cancel terms much faster during the exam.
Updated On: Jun 24, 2026
- \(\frac{13}{99}\)
- \(\frac{14}{99}\)
- \(\frac{16}{99}\)
- \(\frac{20}{99}\)
- \(\frac{25}{99}\)
Show Solution
The Correct Option is B
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
