3. A form has 7 questions, each with 3 possible answers: AGREE (A), DISAGREE (D), or NO OPINION (N). How many different ways can the form be filled with the same number of AGREE's and DISAGREES's?

All of the employees at the acmesoft company are either programmers or salespeople. The programmers are always tell the truth, the salespeople always lie. Threes Acmesoft employees - A, B, and C-were standing together in the hallway. A visitor passed by and asked A. "Are you a programmer or a salesperson?" A mumbled an answer that the visitor could not hear clearly. The visitor then asked B, "what did A say?" B replied. "A said that he is a salesperson."At this point, the third employee, C, said ,"Don't believe B; he is lying! What are B and C? 1/ B and C are both programmers 2/ B is a programmer and C is a salesperson 3/  B is a salesperson and C is a programmer 4/ B and C are both salesperson

Use the following information to answer the next question Leonidas is having a party and is planning to play some great music over the dinner hour. He made a short list of 18 songs that include 10 classical songs and 8 jazz songs. Over the dinner hour it is decided that of the 18 songs, 4 classical songs and 3 jazz songs will be selected, and then arranged into an order to be played. To determine the number of potential music arrangements for the party the following expressions were created: i) 10C4 X 8C3 X 7! ii) 10P4 8P3 iii) (¹0)(3) × 5040 iv) 18P7 v) (10 x 9 x 8 x 7) × (8 × 7 × 6) vi) 11. How many of the above expressions are correct? a) 5 b) 4 (10x9x8x7) (8x7x6) X 4! 3! c) 3 x 7! d) 2

Professor Hermann gives his class 12 potential test questions, he will then put 5 of the 12 questions on the real test. In how many ways can Professor Hermann make up the test?