Counting Methods

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

At  a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

• 180
• 23
• 12
• 60

Find the number of batting orders for 9 players.

• 362,880
• 1
• 81
• 72

Tags

CCSS.HSS.CP.B.9

There are 6 roads from Ponder to Justin, 2 roads from Justin to Halslet, and 3 roads from Haslet to Saginaw.  How many possible routes are there from Ponder to Saginaw using only these roads and no backtracking? 

• 12
• 11
• 18
• 36

Tags

CCSS.8.EE.C.7B

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 0 to 9?

• 9,000,000,000
• 81
• 387,420,489
• 1,000,000,000

A combination lock has 7 digits.  How many distinct combinations does this lock have if the numbers used have to be 0 through 5?

• 279936
• 78125
• 823543
• 16807

How many ways can the letters in the word PARALLEL be arranged?

• 40,320
• 1
• 3360
• 64

How many distinct ways can the letters in the word OPPORTUNITIES be arranged?

• 389,188,800
• 2,028,377,600
• 1,556,755,200
• 16,227,020,800

9 runners are racing. In how many ways can they come in 1^st, 2^nd and 3^rd place?

• 362,880
• 9
• 308
• 504

Tags

CCSS.HSS.CP.B.9

Student council has 24 members.  In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?  (Order matters)

• 5,100,480
• 0
• 42,504
• 5.17 x 10²¹