AMDM A Unit 1 Fundamental Counting Principle

The Social Security number contains nine digits, if the form of 000-00-0000. How many different Social Security numbers can be formed using any numerals from 1 to 9 and numbers cannot repeat?

• 9,000,000,000
• 81
• 362,880
• 1,000,000,000

How many area codes of the form (XYZ)are possible if the digits X and Y can be any number 1-9 and digit Z can be any number 2-9 ?

• 1000
• 729
• 512
• 648

Student ID number consists of 6 characters. The first four characters can be any number 1-9 without restrictions. The last two characters are letters and cannot repeat. How many student IDs are possible? 

• 6,760,000
• 4,264,650
• 6,500,000
• 78

The country of Scitsitats requires the people in their country to have license tags on their car such that the first 3 characters are English letters but no letter may repeat and letters I and O are excluded. The last 3 characters must each be a number 1 – 9 and again no numbers can be repeated. How many license tags are possible?

• 180
• 17, 576, 000

• 12,000,000
• 6,120,576

You are about to take 6 question test. Each question has 4 possible answer choices. How many ways can you answer the test if you answer each question?

• 4096
• 24
• 1296
• 10

How many different three digit alarm codes can be formed for the house alarm if the first digit must be 3, 5 or 7, and all other digits can be any number but numbers cannot repeat.

• 300
• 3000
• 270
• 22

A menu has 4 different sandwiches, with 2 choices of potato chips, 3 types of salad and 5 different beverages. How many different lunch combinations consisting of a sandwich, chips, salad and beverage can be ordered?

• 30
• 17
• 90
• 120

How many 5-digit (numerical) passwords are possible for the school email system?

• 11,424,400
• 10,967,424
• 9000
• 100,000

A suit case combination lock consists of a 4 digit code. Each digit can be any number 0 - 9. The only exception is that all four digits cannot be the same (e.g. the combination can’t be 1111, 2222, etc.) How many combinations are possible on a standard combination lock?

• 10,000
• 9,990
• 5,050
• 40

Ten digit telephone number has a form (XYZ) - ABC-DEFG. In the particular state there are 4 possible area codes (404, 470, 678, and 607). The digit A is restricted to a number 2 through 6. The digits B and C can be any number but they cannot repeat. D,E,F, G have no restrictions. How many phone numbers are possible with these restrictions?  

• 28,800,000
• 25,200,000
• 18,000000
• 28,000,000