* For the first four letters in the English alphabet, a. list the possible permutations of three letters from the four.b. list the possible combinations of three letters from the four.c. Use parts (a) and (b) to obtain 4P3 and 4C3.d. Use the permutations and combinations rules to obtain 4P3 and 4C3. Compare your answers in parts (c) and (d).

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

Assume Amy is making a sandwich for lunch and needs to select her sandwich fixings. She will select two meats out of 5 options, 1 cheese out of 3 options, and exactly 3 or exactly 5 vegetables out of the 7 options. She will also decide whether to add mayo or not. How many ways can she make her sandwich.

Toward the end of a game of Scrabble you hold the letters D,O,G and Q.  You can choose three of these four letters and arrange them in order in how many different ways?

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?