Lesson 4.7 Checkpoint

A standard-issue 2014 New Jersey license plate had three digits followed by three letters. These plates were not allowed to have letters D, T, or X in the fourth position, or the letters I, O, or Q in any position. With these restrictions, how many different license plates were possible in 2014? (LT 4.7.1 #1)

• 10580000

• 1402410240

• 1947792

• 3.71 x 10⁴¹

In the United Kingdom, every resident is issued a national insurance “number” for the national health system and social security. The format of the “number” is two letters, followed by six digits, and then a third letter. The first two letters cannot be D, F, I, Q, U, or V, and the second letter also cannot be O. The last letter is either A, B, C, or D. All six digits can be 0 through 9, with no restrictions. How many national insurance numbers can be issued with these restrictions? (LT 4.7.1 #2)

• 1520000000

• 3.41 x 10¹³

• 94143280

Suppose you have 6 homework assignments to complete one night. In how many different orders can you complete all of the assignments? (LT 4.7.2 #1)

• 720

• 1

• 36

Mario has 10 science fiction novels on a shelf in his bedroom. How many different ways are there for him to arrange the books on the shelf? (LT 4.7.2 #2)

• 3628800

• 1

• 90

Declan has 100 songs on his MP3 player. He is going for a run and has time to listen to 8 songs while he runs. Declan decides to use the MP3 player’s random shuffle feature to determine which songs will play, and in what order. (The random shuffle feature does not allow any song to be played twice.) How many different lists of 8 songs are possible? (LT 4.7.3 #1)

• 7.50 x 10¹⁵

• 1.86 x 10¹¹

• 40320

Mr. Vellman has a test bank with 75 multiple-choice questions on Lesson 4.7. The test bank comes with a random generator that will select and arrange questions to make different versions of a test. How many different versions of a 10-question multiple-choice test on this lesson could Mr. Vellman make? (LT 4.7.3 #2)

• 3.01 x 10¹⁸

• 8.29 x 10¹¹

• 3628800

• 750