Question

1 When a pair of dice is thrown once the number of elements of the sample space equals a) 2x2 b) 2* 6 c) 6x6 d) 2 2. A group of tourists are offered 6 sightseeing tours on each of 3 days. A tourist ) can arrange to go on a sightseeing tour (a -s-a3,*) İn a) 2* ways b) 6 ways c) 3 x6 ways d) 3ơ ways 3. The number of ways in which we can select a president and a secret among a group of 11 students is a) 11x1o b) 11 c) C2 d) 11! 4 If a multiple-choice test consists of 5 questions each with 4 possible answers of which only 1 is correct. Then the number of vways in which a student choose one answer to each question equals 5 a) 5! b) 4! c) 4 d) 5 5. How many different letter arrangements can be formed using the letters of the wordLAYOUT? b) 61/3 a) 6! How many different numbers can be formed from the digits 1, 3, 6. 7, 9 such that each number contains 3 digits and repetitions are permitted? d) 1 6. d) 3 In a competition (un-a), the 9 finalists (yshei.-yai) consist of 4 boys and 5 girls. The number of sample points in the sample space S for the number of possible orders at the conclusion of the contest for the first 3 positions equals 7. b) P d) 3! 8. The number of ways that no two students will have the same birth date in a class of size 40 equal a) 40 openings in an accounting firm equals a) 8! c) 36s d) 12! 9. The number of ways to select 3 candidates from 8 equally qualified recent graduates for d) 3 10. A young boy asks his mother to get five Game-BoyT* cartridges from his collection of 10 arcade and 5 sports games. His mother will get 3 arcade and 2 sports games in number of ways equals a) 2x3 10 b) 10xS d) 10x3 11. If an experiment consists of throwing a die and then drawing a letter at random from the English alphabet, the possible number of elements in the sample space equals b) 6x26 c) 26 d) 6x2s

Answer 1

1. The number of outcomes on each die is 6.So when 2 dice are thrown simulataneously, the toal number of possible oucomes will be 6*6 ways (option c)

2. 6 sightseeing tours in each of the 3 days so the tourist can choose to visit any 6 on the first, the second and the third day so there are 6³ ways to do so. (option b)

3. Out of the group of 11 students any one can be chosen as the president.This can be done in 11 ways and a secretary can be chosen from the remaining 10 in 10 ways. So the total number of possible ways is 11*10 ways (option a)

4. 5 questions in which each question can 4 alternatives of which only one is correct. SO the number of ways in which a student can respond to each question is 4. Hence, for 5 questions the total number of such combination of choices is 4⁵ (option c)

5. The letters in the word LAYOUT are distinct so the total number of possible arrangements is 6! (option a)

6. We have 5 numbers that are 1,3,6,7,9 and repitions are allowed.So for the 3 digit numbers the units digit can be chosen in 5 ways, the tens digit can also be chosen in 5 ways and also for the hundreds digit.Hence, there are 5³ such numbers (option c)