A quiz consist of 2 true-or-false questions 3 are multiple choice questions. The multiple choice questions have 3 options each. How many ways can a student complete the quiz?a.36b.162c.108d.18A secrete code consist of 2 digits, followed by 2 letters, followed by 1 of the following symbols @,#,%, and &. Digits and letters cannot repeat. a.243,360b.260,000c.234,000d.270,400How many distinct arrangements can you make using the letters in the word EXPERIMENT?a.1,209,600b.3,628,800c.725,760d.604,800How many ways can a dance instructor send 4 of her 11 students to a summer dance program?a.330b.720c.7920d.1980There are 5 keys on a key chain. 1 of the keys start a car. A random key is chosen. What is the probability that it starts the car?a.25%b.5%c.20%d.15%The probability of choosing a winning card from a stack of cards is 2.9%. What is the probability of choosing the losing carda.87.1%b.92.9%c.99.71%d.97.1%
Accepted Solution
A:
A. For the first two questions, there are 2 choices, true and false. The three questions will have 3 choices. The number of ways that student can complete the test is,
n = 2 x 2 x 3 x 3 x 3
n = 108
Answer: C. 108
B. From 0 to 9, there are 10 digits. There are also 26 and as per given, there are 4 symbols. The number of ways that the code can be made is,
n = 10 x 9 x 26 x 25 x 4
n = 234,000
Answer: C. 234,000
C. In the word, EXPERIMENT, there are 10 letters. Three of which are letter Es. The number of ways that the letters can be arranged is,
n = 10!/3!
n = 604,800
Answer: D. 604,800
D. If the arrangement is not important and that only the combination is important, the number of ways that the instructor can send 4 out of the 11 is,
n = 11C4 = 330
Answer: A. 330
E. If only one of the five keys can start the car then, the probability that the chosen key can start the car is equal to the ratio of the number of key to the total number of keys.
n = (1/5)(100%) = 20%
Answer: C. 20%
F. The events of picking the winning card and picking or choosing the losing card are complementary events such that the sum of their probabilities should be equal to 1 or 100%.