Question

In how many ways can the letters of the word Permutations be arranged if (i) the words starts with P and end with * (ii) Vowels are all together.

Answer 1

n = 12

T repeats = 2 times,

(i) the word starts with P and ends with *

(P ......... (5)

Total words = 9!/2! = 9 × 8 × 7 × 6 × 5 × 4 × 3 = 1,81,440 ways

(ii) Vowels are together: vowels = E,U,A,I,O = * together

∴ they form 1 group remaining +7/8 letters

∴ Total words = 8!/2! = 8 × 7 × 6 × 5 × 4 × 3 = 20,160 ways.