Example What is the number of permutations of the letters in the word Mississippi?
▪ Example What is the number of permutations of the letters in the word Mississippi?
LetS={n1°a1n2°a2y…,nkal},and n=n+n2+.+nk=s, then the number n of r permutations of s equals r>n (2n!(n1!n2…n") t-n (3)k n:≥ r for each i=12n (4)Ifr<n, there is, in general, no simple formula for the number of r-permutations of Nonetheless a solution can be obtained by the technique of generating functions, and we discuss this in 4.6
▪ Let S={n1 •a1 ,n2 •a2 ,…,nk •ak }, and n=n1+n2+…+nk=|S|，then the number N of rpermutations of S equals ▪ (1)0 r>n ▪ (2)n!/(n1 !n2 !…nk !) r=n ▪ (3)kr ni r for each i=1,2,…,n ▪ (4)If r<n, there is, in general, no simple formula for the number of r-permutations of S. ▪ Nonetheless a solution can be obtained by the technique of generating functions, and we discuss this in 4.6