Question

part one - multiple choice (circle the best answer)

1. a library code is 3 digits (0 - 9) followed by two letters. how many codes are possible?

a. 468 b. 492,804 c. 527,000 d. 676,000

1. a test has 30 multiple - choice questions with 4 choices each. which expression represents the

total number of ways to answer all questions?
a. 30 · 4 b. 30! c. 30p4 d. 4^{30}

1. a 7 - card hand is dealt from a 52 - card deck. which expression represents the number of

possible hands?
a. 52 · 7 b. 52! c. 52p7 d. 52c7

1. how many distinct arrangements of the letters in probability (11 letters, with repeats) are

possible?
a. 1,663,200 b. 7,241,600 c. 9,979,200 d. 39,916,800
use this for questions 5 and 6 below: a basket contains 8 green apples, 11 red apples, 5 nectarines, and 12
oranges. mark chooses a piece, eats it, then selects another (without replacement).

1. p(green then nectarine)

a. 2363 b. 5162 c. 1336 d. 263

1. p(two oranges)

a. 19 b. 435 c. 11105 d. 68105
use the honor - roll table:
. assume totals: school total = 200. honor roll by grade: 9th = 25, 10th = 30, 11th = 19, 12th = 26.

1. p(honor roll | 11th grader)

a. 19200 b. 1975 c. 1950 d. 19105

Explanation:

Step1: Calculate the number of ways for digits and letters

For the 3 - digit part (each digit has 10 choices from 0 - 9), the number of ways is \(10\times10\times10=10^{3}\). For the 2 - letter part (each letter has 26 choices), the number of ways is \(26\times26 = 26^{2}\).

Step2: Use the multiplication principle

By the multiplication principle (if one event can occur in \(m\) ways and another independent event can occur in \(n\) ways, then the two events together can occur in \(m\times n\) ways), the total number of library codes is \(10^{3}\times26^{2}\).

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Answer:

D. 676,000