The number of permutations of the letters of the word RICOCHET such that no letter occurs in the same position in the permuted word as in the original. Solution Number of way to arrange C\'s in the given eight positions, such that they don\'t appear in their original positions, are: 8C2 -14 = 28 - 14 = 14 Out of remaining 6 letters 4 can be arranged in the remaining 4 positions such that they don\'t appear in their original positions are (4!/2) = 24/2 = 12 Remaining 2 letters can be arranged in the remaining two positions such that they don\'t reappear in their original positions in (2!/2) = 1 way Therefore, total number of ways to arrange the letters of the given word, such that none of the letters appear in its original position, are 12*14*1 = 168 Therefore, final answer is 168..