### Instruction: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Answer Choices: (A) 720 (B) 127 (C) 137 (D) 129 (E) 112 Please respond by writing a program in Python.### Response: import math


# The word 'LEADING' has 7 letters, and 3 of them are vowels (E, A, I).
# If we consider the vowels as a single entity, we have 5 entities to arrange (L, N, D, G, VOWELS).
# These 5 entities can be arranged in 5! ways.
# The 3 vowels can be arranged among themselves in 3! ways.
# So, the total number of arrangements is 5! * 3!.

total_arrangements = math.factorial(5) * math.factorial(3)
print(total_arrangements)