Please answer the questions in red.

CSS 220 Module 1 In-Class Problems (Total 10 points) In each place, you should find how many different numbers can be placed. 7x 6 x 5 x 4 = 840 1) How many permutations are there for letters (c, o, m, p, ut, e,r) that start with a consonant and is followed by a vowel in the second position? (2 pts) b. Find an answer using a permutation symbol. Pm a. 5 3 6 5 4 3 2 1 4) How many ways can we write a list of 10 numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10) without repeating any? (2 pts) I think you can handle this question without an answer. Provide your answer. T Consonant {c, m, p, t,r} 1 1 1 Vowel {o, u, e) {rest of the letters after two letters taken from the 1st and 2nd positions) 5) How many different 7-character license plates are possible if they must include exactly three letters and four numbers. The first, middle, and last characters in the license plate should be letters. Letters must be upper cases. (2 pts) First Middle Last 5x 3 x 6 x5 x 4x 3 x 2 x 1 = 10800 b. How many different letter strings will be generated if the 3rd position in this letter strings is also a consonant. 26 10 9 25 8 7 24 5 3 Z Total Number of uppercase letters: 26 {A, B, C, Total number of digits: 10 {0, 1, 2, 3, ....... 9} 1 T Consonant Vowel {c, m, p, t,r} {o, u, e) 1 1 Consonant {rest of the letters after two letters taken from the 1st and 2nd and 3rd positions.} 1. No repetition: 26 x 10 x 9 x 25 x 8 x 7 x 24 2. What if it allows repetition? Provide your answer. What I showed you in class was to generate license plate numbers without repetition using specific letters and numbers. Assume that you have {a,b,c} and {1,2,3,4}. Then, possible license plate numbers are: 3x4x3x2x2x1x1 = 144 First Middle Last 2) How many ways can you draw a face card from a standard 52-card deck? Aces are not considered a face card. (1 points) a. For one time draw, the chance of having a face card is to find total number of the face cards. There are 3 kinds of face cards, and each type has 4 cards. => 3X4 =12 b. How many ways can you draw a face card consecutively from a standard 52-card deck? (No repetition) DOOR 3 4 3 2 2 1 1 Letters number number Letters number number Letters 1st draw 2nd draw 3) a. How many ways can we write a list of 4 numbers from (1, 2, 3, 4, 5, 6, 7) without any repeating? (2 pts) 7 6 5 4 6) Evaluate P7 Hint: P = (1 pt) (n-m)! Compute the permutation PA using the Hint