1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days
8104911739
For Business Enquiry

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this toll free number

022-62211530

Mon to Sat - 11 AM to 8 PM

Permutations And Combinations

Share this:

Permutations And Combinations PDF Notes, Important Questions and Formulas

Introduction to permutations and combinations: 

  

Permutations and Combinations:
 

Permutations

Combinations

Arrangement in a definite. Order is considered

Selection is made irrespective of arrangement

Ordering of the objects is essential

Ordering of the selected object is immaterial

Permutation corresponds to only one combination

Combination corresponds to many permutations

Number of permutations exceeds the number of combinations

Number of combinations is lesser than the number of permutations

 

FUNDAMENTAL PRINCIPLE OF COUNTING

 

Multiplication principle

If one operation can be performed in m ways and simultaneously another operation can be performed in n ways the number of ways of performing the two operations will be m × n.

 

FUNDAMENTAL PRINCIPLE OF ADDITION

If one operation can be performed in m-ways and another operation can be performed in n ways then either first or second operation can be happened in (m + n) ways.

 

Permutations (arrangements)

The number of permutations of n objects, taken r at a time is the total number of arrangements of ‘r’ objects taken from ‘n’ objects where order of arrangements matters. In other words it is total possible ordered sets of r elements selected from given ‘n’ elements.

 

A. Repetition is not allowed

    (i) Number of ways in which n distinct object can be arranged amongst themselves is
         = n . (n-1) (n-2) ................ 3.2.1 =m!

    (ii) Number of ways in which we can arrange ‘n’ object taken r at a time

         begin mathsize 12px style equals space straight n open parentheses straight n minus 1 close parentheses open parentheses straight n minus 2 close parentheses.... open parentheses straight n minus straight r plus 1 close parentheses equals fraction numerator straight n factorial over denominator open parentheses straight n minus straight r close parentheses factorial end fraction
equals straight P presuperscript straight n subscript straight r equals straight P open parentheses straight n comma straight r close parentheses equals straight A presuperscript straight n subscript straight r equals straight A open parentheses straight n comma straight r close parentheses end style

 

B. Repetition is allowed. 

The number of arrangements of n different objects, taken `r' at  a time, when each object may occur any number of  timesbegin mathsize 12px style stack stack straight n. text   n.  n  end text....... text n end text with bottom square bracket below with straight r text  terms end text below equals straight n to the power of straight r end style ways.

 

Circular Permutation

The number of circular permutations of n different things taken all at a time is (n - 1)!
If clockwise & anti-clockwise circular permutations are considered to be same, the it is begin mathsize 12px style fraction numerator left parenthesis straight n minus 1 right parenthesis factorial over denominator 2 end fraction end style

Show more

IIT JEE Mathematics Permutations And Combinations Video Solutions by Experts

IIT-JEE Tests & Papers Solutions

Mathematics syllabus

Purchase Our Experts Course Packages

Enroll now to crack IIT-JEE

Testimonials

Ask Experts for IIT-JEE

Queries asked on Sunday and after 7 pm from Monday to Saturday will be answered after 12 pm the next working day.

View More

Chat with us on WhatsApp