# Permutations and Combinations

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The NCERT solutions for Class 11 Maths consists of a chapter called Permutations and Combinations that has been explained by Extramarks with Animations, Mindmaps and other learning modules. Students who are weak at Maths don’t have to feel anxious about the subject anymore. Extramarks gives all necessary study help to make even the most difficult concepts easy and fun to learn. Permutations and Combinations in Class 11 is a chapter that can really help the students stretch few good scores if understood properly. All thanks to Extramarks!

A permutation is an arrangement in a definite order of a number of objects, taken some or all at a time. Fundamental principle of counting states that m×n is the total number of ways in which two events occur where m and n are the number of ways in which first and second event occur respectively. If there are two mutually exclusive events, such that they can be occurred independently in m and n ways respectively, then either of the two events can be occurred in (m + n) ways. Product of the first ‘n’ natural numbers is n!. It is read as ‘n factorial’ or ‘factorial n’. The number of all permutations of n different objects, taken all at a time is n!. The number of permutations of n different objects taken r at a time, where repetition is not allowed, is given by nPr = n! / (n – r)! , 0 ≤ r ≤ n The number of permutations of n different objects taken r at a time, where repetition is allowed, is nr. The number of permutations of n objects, where p objects are of the same kind and rest are all different is (n! / p!). The number of permutations of n objects taken all at a time, where p1 objects are of first kind, p2 objects are of the second kind, …, pk objects are of kth kind and rest, if any, are all different is (n! / p1!p2!...pk!). A combination is a selection made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time is given by nCr = n! / r!(n – r)! , 0 ≤ r ≤ n.

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