If one quarter of all the subsets containing three elements of the set A-a1-a2-a3-an contains the element a3- then the value of n is

There are ^nC_3 subsets of set A, containing three elements. nbsp; If a_3 is always included, then there are ^n 1C_2 subsets of set A. Given, 14×^nC_3=^n 1C_2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Combination with Restrictions

If one quarte...

Question

If one quarter of all the subsets (containing three elements) of the set $A = {a_{1}, a_{2}, a_{3}, \dots, a_{n}}$ contains the element $a_{3},$ then the value of $n$ is

10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

12

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

14

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $12$
There are $^{n} C_{3}$ subsets of set $A,$ containing three elements.
If $a_{3}$ is always included, then there are $^{n - 1} C_{2}$ subsets of set $A .$
Given, $\frac{1}{4} \times^{n} C_{3} =^{n - 1} C_{2}$
$\Rightarrow \frac{n (n - 1) (n - 2)}{24} = \frac{(n - 1) (n - 2)}{2} \Rightarrow n = 12$

Suggest Corrections

Similar questions

Q. If one quarter of all three element subsets of the set

A = a_{1}, a_{2}, a_{3} . . ., a_{n}

contains the element

a_{3}

then n

=

Q. If one quarter of all the subsets (containing three elements) of the set

A = {a_{1}, a_{2}, a_{3}, \dots, a_{n}}

contains the element

a_{3},

then the value of

n

Q. If 20% out of the subsets ( subsets containing exactly three elements) of the set

A = {a_{1}, a_{2}, a_{3} . . . . . a_{n}}

contain

a_{1},

then the value of

n

Q. The number of all three element subsets of the set

{a_{1}, a_{2}, a_{3} \dots, a_{n}}

which contain

a_{3}

is:

Q. The total number of three element subsets of the set {

a_{1}, a_{2}, a_{3} . . . a_{n}

} which contain

a_{3}

Join BYJU'S Learning Program

Explore more

Combination with Restrictions

Standard XII Mathematics

Join BYJU'S Learning Program

If one quarter of all the subsets (containing three elements) of the set A={a1,a2,a3,…,an} contains the element a3, then the value of n is

The correct option is B 12There are nC3 subsets of set A, containing three elements. If a3 is always included, then there are n−1C2 subsets of set A. Given, 14×nC3=n−1C2 ⇒n(n−1)(n−2)24=(n−1)(n−2)2⇒n=12

If one quarter of all the subsets (containing three elements) of the set $A = {a_{1}, a_{2}, a_{3}, \dots, a_{n}}$ contains the element $a_{3},$ then the value of $n$ is