One other approach to solve this problem will be fix positions for 5 vowels in alphabetical order. Now there are 6 positions to place constant. (i.e. C V C V C V C V Where C is constant and V is vowel). Now find the number of permutations of non-negative integer solutions for equation X1 + X2 + X3+ X4+ X5+ X6 = 6 since there are 6 places to be filled(X1, X2..... denotes number of constants at position 1,2.... respectively) and and the sum of elements at those 6 places will be 6(since there are 6 constants to be placed). So r = 6 and n = 6 here. Putting it in formula (n + r - 1) P (r - 1), i.e. 11 P 5 = 332640. Since two constants are same removing their permutation final answer is 332640/2 = 166320