You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.

Input: Consider Input: Question: A six-character password consists of three letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?

 Option A: 5,040

 Option B: 2,228,720

 Option C: 22,226,000

 Option D: 22,237,440

 Option E: 22,464,000

Output: Option E


Input: Consider Input: Question: A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?

 Option A: 13/2

 Option B: 19/2

 Option C: 21/2

 Option D: 15/2

 Option E: None

Output: Option C


Input: Consider Input: Question: The probability that A speaks truth is 1/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?

 Option A: 13/35

 Option B: 18/38

 Option C: 18/36

 Option D: 18/16

 Option E: 18/31


Output: Option A