Exercise 28 Page 929

Let's begin by recalling the definitions of a permutation and a combination.

• Permutation: An arrangement of elements in a particular order.
• Combination: An arrangement of objects in which order does not matter.

  Both permutations and combinations can be used when selecting elements from a given set. The only difference between them is that, in the case of a permutation, the order of selection matters while in the case of a combination the order is not important. Let's give an example for each one to see this difference more clearly.

  	Example	Does the Order Matter?
  Permutation	Forming a two-digit number	Yes ✓
  Combination	Drawing winners of a lottery if the value of the prize is equal for all winners	No *

  This difference can be also noticed in the Permutation Formula and the Combination Formula. In these formulas, n is the number of elements and r is the number of items we want to have in a chosen set.

  Number of Permutations	Number of Combinations
  _nP_r=n!/(n-r)!	_nC_r=n!/(n-r)! r!

  Here we can notice an extra term r! in the denominator of the second formula. This indicates that the number of combinations will always be less than or equal to the number of permutations for the same n and r.