CET Permutation and Combination Questions with Solutions – Page 3

In how many ways can the alphabets of the word ATTITUDE be rearranged in such a way that no two T's are adjacent to each other ?

P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is no direct path between P and S, while there are few direct paths between Q and R, and between R and S. One can travel from P to S either via Q, or via R, or via Q followed by R, respectively, in exactly 62 possible ways. One can also travel from Q to R either directly, or via P, or via S, in exactly 27 possible ways. Then, the number of direct paths between Q and R is.

In how many ways can the letters of the word MATHEMATICS be arranged so that all the vowels always come together?