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Advanced Math

How many permutations of size r can be drawn from a collection of n objects? Please give a short explination

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Subject Discrete Structures

How many permutations of size r can be drawn from a collection of n objects? Please give a short explination

Expert Solution

Step 1

If n is a positive integer and r is a whole number, such that r < n, then P(n, r) represents the number of all possible arrangements or permutations of n distinct objects taken r at a time. In the case of permutation without repetition, the number of available choices will be reduced each time.

P(n, r) = n(n-1)(n-2)(n-3)……..upto r factors

P(n, r) = n(n-1)(n-2)(n-3)……..(n – r +1)

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