Question:
The number of all three elements subsets of the set $\{a_1, a_2, a_3 . . . a_n\}$ which contain $a_3$ is
The number of all three elements subsets of the set $\{a_1, a_2, a_3 . . . a_n\}$ which contain $a_3$ is
Updated On: Jan 30, 2025
- $^nC_3$
- $^{n - 1} C_3$
- $^{n - 1} C_2$
- None of these
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The number of three elements subsets containing $a^3$ is equal to the number of ways of selecting $2$ elements out of $n - 1$ elements. So, the required number of subsets is $^{n -1}C_2$.
Was this answer helpful?
2
0
Top Questions on types of sets
- Let S be the set of values of λ, for which the system of equations
6λx – 3y + 3z = 4λ2 ,
2x + 6ly + 4z = 1,
3x + 2y + 3λz = l has no solution. Then 12\( ∑ _{λ ∈ S}\) | λ | 12 ∑ λ ∈ | λ | is equal to ________ .- JEE Main - 2023
- Mathematics
- types of sets
- The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is
- JEE Main - 2023
- Mathematics
- types of sets
- Total number of elements in the power set of a set \( A \) containing 15 elements is:
- COMEDK UGET - 2021
- Mathematics
- types of sets
- Two sets $A$ and $B$ are as under: $A = \{(a, b) \in R \times R : |a - 5| < 1$ and $|b - 5| < 1\} $; $B = \{(a, b) \in R \times R : 4(a - 6)2 + 9(b - 5)^2 \leq 36\}$. Then
- JEE Main - 2018
- Mathematics
- types of sets
- The number of proper subsets of a set having $n + 1$ elements is
- COMEDK UGET - 2014
- Mathematics
- types of sets
View More Questions
Questions Asked in BITSAT exam
- A dust particle of mass 4 × 10⁻¹² mg is suspended in air under the influence of an electric field of 50 N/C directed vertically upwards. How many electrons were removed from the neutral dust particle? (g = 10 m/s²)
- BITSAT - 2025
- Electrostatics
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Vector Algebra
- A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both are red?
- BITSAT - 2025
- Probability
- The electric field at a point on the axis of a uniformly charged ring of radius R at a distance x from its center is given by: \[ E = \frac{1}{4\pi\epsilon_0} \cdot \frac{2\pi kQx}{(x^2 + R^2)^{3/2}}. \] If x = 2R, what is the magnitude of the electric field?
- BITSAT - 2025
- Electrostatics
- A simple pendulum has a time period of 2 s on Earth's surface. What is its time period at a height equal to the Earth's radius (R)? (Acceleration due to gravity at height h is \( g_h = \frac{g}{(1 + h/R)^2} \)).
- BITSAT - 2025
- Mechanics
View More Questions