Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.

Problem: the average age of 15 students of a class is 15 years. out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years, the age of the 15 th student is
Options: a. 17, b. 12, c. 13, d. 14, e. 15
a

Problem: find the smallest number that should be multiplied with 54000 to make it a perfect cube.
Options: ['a. 4', 'b. 5', 'c. 6', 'd. 3', 'e. 7']
a

Problem: 18 business executives and 7 chairmen meet at a conference. if each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place ?
Options: a. 144, b. 131, c. 279, d. 90, e. 45

c