Example: Let S=( 2.X133'X2, Determine the number 4-permutations of s Solution: Let pr be the number r-permutations of s, g(x)=(1+x+x2/2!)(1+x+x2/2!+x3/3!) Note: pr is coefficient of x/r!. Example: Let S=(2 X13 3 X2, 4 X33. Determine the number of 4-permutations of s so that each of the 3 types of objects occurs even times. Solution: Let pa be the number 4-permutations, g(x)=(1+x2/2)(1+x2/2)(1+x2/2!+x4/4!)▪ Example：Let S={2·x1 ,3·x2 }，Determine the number 4-permutations of S. ▪ Solution: Let pr be the number r-permutations of S, ▪ g(x)=(1+x+x2 /2!)(1+x+x2 /2!+x3 /3!) ▪ Note: pr is coefficient of xr /r!. ▪ Example：Let S={2·x1 ,3·x2 ,4·x3 }. Determine the number of 4-permutations of S so that each of the 3 types of objects occurs even times. ▪ Solution: Let p4 be the number 4-permutations, g(x)=(1+x2 /2!)(1+x2 /2!)(1+x2 /2!+x4 /4!)