How many ways are there of arranging the 26 letters of the alphabet so that none of the words be, lap, scum, or third appear as consecutive letters in the arrangement? You do not need to explicitly evaluate your answer.

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

Of the 58 students in a mathematics​ class, 22 are taking​ French, 24 are taking​ German, and 7 are taking both French and German.   How many students in the mathematics class are taking neither French nor​ German?   nothing students

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?