Theorem 4.5: For n and r positive integers with rsn, 令p(n,r)=n(n-1)(n-r+1 4. Proof: In constructing an r-permutation of an n element set, we can choose the first item in n ways the second item in n-l ways whatever choice of the first item,.., and the rth item in n-(r-1) ways whatever choice of the first r-l items. By the multiplication principle the r items can be chosen in n(n-1)….(n-r+1)ways. ☆ We define n!b n !=n(n 1).2°1 o with the convention that 0:=l.Thus p(n, r=n /(n-r).❖ Theorem 4.5: For n and r positive integers with rn, ❖ p(n,r)=n(n-1)…(n-r+1) ❖ Proof:In constructing an r-permutation of an n￾element set, we can choose the first item in n ways, the second item in n-1 ways whatever choice of the first item,… , and the rth item in n-(r-1) ways whatever choice of the first r-1 items. By the multiplication principle the r items can be chosen in n(n-1)…(n-r+1) ways. ❖ We define n! by ❖ n!= n(n-1)…2•1 ❖ with the convention that 0!=1.Thus p(n,r)=n!/(n-r)!