﻿ Let X is a set containing n elements. A subset P of set X is chosen at random. The set X is then reconstructed by replacing the elements of set Pand another set Q is chosen at random. Find  number of ways to  chosenP and Q such that P ∪ Q contains exactly r elements. : Kaysons Education

# Let X is A Set Containing N Elements. A Subset P of Set X is Chosen At Random. The Set X is Then Reconstructed By Replacing The Elements Of Set Pand Another Set Q is Chosen At Random. Find  number of Ways To  chosenP and Q such That P ∪ Q Contains Exactly r elements.

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

Q has r elements. It means r elements out of n elements should be present in either P or in Q or both. r elements out of n elements can be selected in ways = nCr

Each of these  elements has 3 choice

Rest (n – r) elements has 1 choice i.e. neither go in P nor in Q

⇒  Number of ways to select P and Q such

#### SIMILAR QUESTIONS

Q1

Find the sum of all four-digit numbers that can be formed using digits 0, 1, 2, 3, 4, no digits being repeated in any number.

Q2

There are three papers of 100 marks each in an examination. Then the no. of ways can a student get 150 marks such that he gets atleast 60% in two papers

Q3

If m parallel lines in plane are intersected by a family of n parallel lines. Find the number of parallelograms formed.

Q4

There are n concurrent lines and another line parallel to one of them. The number of different triangles that will be formed by the (n + 1) lines, is

Q5

Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them, is

Q6

The sides AB, BC and CA of a triangle ABC have a, b and c interior points on them respectively, then find the number of triangles that can be constructed using these interior points as vertices.

Q7

Let is a set containing n elements. A subset P of set X is chosen at random. The set X is then reconstructed by replacing the elements of set Pand another set Q is chosen at random then find the number of ways to form sets such that

Q8

In how many ways can 12 books be equally distributed among 3 students?

Q9

10 different toys are to be distributed among 10 children. Total number of ways of distributing these toys so that exactly 2 children do not get any toy, is equal to:

Q10

There are 20 persons among whom are two brothers. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two brothers.