(2) m+m2 +.mI=1 k ≥0 ating Is the number of r-permutatio ns of s given g(x)=gn(x)' g n,(x).. gn(x), where for i=1, 2,., K, gn(x)=1+x+x22+…,+x"!n;! ) The coefficient of x/r!ingn(x)gn2(x)∵…gn(x)is m.+m.+…m=rm1!m2!…mk m≥0▪ Theorem 4.17: Let S be the multiset {n1·a1 ,n2·a2 ,…,nk·ak } where n1 ,n2 ,…,nk are non￾negative integers. Let br be the number of r￾permutations of S. Then the exponential generating function g(x) for the sequence b1 , b2 ,…, bk ,… is given by ▪ g(x)=gn1 (x)·g n2 (x)·…·gnk (x)，where for i=1,2,…,k, ▪ gni (x)=1+x+x2 /2!+…+xni/ni ! . ▪ (1)The coefficient of xr /r! in gn1 (x)·g n2 (x)·…·gnk (x) is   + + = 0 1 2 1 2 ! ! ! ! i k m m m m r m m mk r   is the number of r - permutatio ns of S ! ! ! ! (2) 0 1 2 1 2   + + = i k m m m m r m m mk r  