Question 22 of 42intermediate🔧 ApplyNumerical5 marks
In how many ways can the letters of the word PERMUTATIONS be arranged if the (i) words start with P and end with S, (ii) vowels are all together, (iii) there are always 4 letters between P and S?
(i)
Answer
1814400
(ii)
Answer
2419200
(iii)
Answer
25401600
Explanation
This question from Exercise 6.3 tests permutations with restrictions. The word PERMUTATIONS has 12 letters with T repeated 2 times. The vowels are E, U, A, I, O (5 distinct vowels). Each part applies different constraint techniques: fixing positions for (i), grouping for (ii), and positional constraints for (iii).