Find the number of ways to arrange each letter of the

Solution

ATQ,

Word: RECREATION Letters: R, E, C, R, E, A, T, I, O, N Vowels: E, E, A, I, O Consonants: R, R, C, T, N Step 1: Treat all vowels as one block Items to arrange → [VOWELS], R, R, C, T, N Total = 6 items, R repeated twice Ways = 6! / 2! = 720 / 2 = 360 Step 2: Arrange the vowels inside the block Vowels → E, E, A, I, O Total = 5 letters, E repeated twice Ways = 5! / 2! = 120 / 2 = 60 Step 3: Total arrangements Total = 360 × 60 = 21,600