Let $S$ be a group of all permutations of the letters $U,N,I,V,E,R,S,I,T,Y$ such that letter $I$ is fixed.
Are the statements given below true or false?
a: There exists an element of order 21.
b: There exists an element of order 11.
First of all, I don't know what permutations looks like if elements repeat. But, still I think that if I look at permutation group made of $U,N,V,E,R,S,T,Y$ then, it has 8! elements hence, no element of order 11 by Lagrange theorem. Also, order 21 element would be made of two disjoint cycles with 3 elements and 7 elements, respectively, which is impossible here. So, a false as well.
Am I correct?