Home
Class 12
MATHS
Let S={1,2,3, . . .,n}. If X denotes the...

Let `S={1,2,3, . . .,n}`. If X denotes the set of all subsets of S containing exactly two elements, then the value of `sum_(A in X) ` (min. A) is given by

A

`.^(n+1)C_(3)`

B

`.^(n)C_(3)`

C

`(n(n^(2)-1))/(6)`

D

`(n(n^(2)-3n+2))/(6)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`underset(A in X)(sum)` minA
`underset(r=1)overset(n-1)(sum)r(n-r)=n underset(r=1)overset(n-1)(sum)r-underset(r=1)overset(n-1)(sum)r^(2)`
`=(n(n-1)n)/(2)-((n-1)n(2n-1))/(6)`
`=((n+1)*n*(n-1))/(1*2*3)=.^(n+1)C_(3)=(n(n^(2)-1))/(6)`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|15 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

Similar Questions

Explore conceptually related problems

Prove that the number of all subsets of a finite set of n element is 2^(n) .

Let S be a set containing 10 distinct elements, then the total number of distinct functions from S to S is:

Prove, by Induction, that the number of all the subsets of a set containing n distinct elements, is 2^n .

Let S={1, 2, 3,4}. The total number of unordered pairs of disjoint subsets of S is equal to :

Let S={1,2,3,4} . The total number of unordered pairs of disjoint subsets of S is equal

A set contains 2n+1 elements. The number of subsets of this set containing more than n elements :

Let A and B be two sets containing 3 and 4 elements respectively. The number of functions from A to B is :

Let A and B be too sets containing four and two elements respectively then the number of subsets of set AxxB having atleast 3 elements is

If A and B two sets containing 2 elements and 4 elements, respectively. Then, the number of subsets of A xx B having 3 or more elements, is

Write down all the subsets of the following set :- {1,2,3}