Consider the given factorial expression and evaluate it. $\frac{(7n +1)!}{(7n)!}$

Enumerate the first three terms of the resulting expression if you are to apply binomial expansion to the following. (h - 3w)¹²

Evaluate the following expression: (₆C₄ x ₉C₁)/₁₂C₄

Work out the probability of getting a number less than 1 when a die is rolled.

A miniature Ferris wheel has twelve seats equidistant with one another along the wheel's circumference and has a shaft that points toward the north. At any given time after being spun, this object is designed so that a shaft always points to any of the twelve seats with a fair probability. These seats are labeled "A" to "L". Find the probability that the shaft points toward a seat labeled by a vowel letter or a letter from "A" through "F".