The number of ways you can choose a president, vice-president, and secretary from a class of seven students is P(7,3) = 7 × 6 × 5 = 210. Note that the number of arrangements of n distinct objects is P(n,n) = n!. This number can be obtained as 5 × 4 = 20, because there are five choices for the first letter, and after that is removed, four choices remain for the second letter, You are chooosing the first letter and the second letter, hence this is an example of the multiplication (and) rule. ab, ac, ad, ae, ba, bc, bd, be, ca, cb, cd, ce, da, db, dc, de, ea, eb, ec, ed. For example P(5,2) = 20 because there are 20 ordered pairs from the letters abcde, viz. P(n,r) denotes the number of distict arrangements of r objects from n objects. It is manifest that 1! = 1, and we define 0! = 1.Ī permutation is an ordering or arrangement of objects. It is convenient to define n factorial, denoted as n! as the product of the first n positive integers. Permutations and combinations Permutations and combinations
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