instruction:
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.
question:
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
answer:
Option E


question:
Question: A committee of 5 people is to be selected from 7 people. How many different committees are possible?

 Option A: 21

 Option B: 40

 Option C: 56

 Option D: D.168

 Option E: 336
answer:
Option A


question:
Question: Stephanie wants to buy lipsticks. Each lipstick costs $20. How much will she pay if she decides to buy 5 lipsticks?

 Option A: $500

 Option B: $100

 Option C: $20

 Option D: $10

 Option E: 0
answer:

Option B