This history question requires analysis of historical events, causes, and consequences. The detailed answer below provides context, evidence, and a well-structured explanation.
ScanSolve AI Answer
Here are the solutions to your problems: 1. A password consists of 4 letters followed by 3 digits. How many different are possible? Step 1: Determine the number of choices for each position. For letters, there are 26 possible choices (A-Z). For digits, there are 10 possible choices (0-9). Assuming repetition is allowed for both letters and digits. Step 2: Calculate the total number of possibilities for the letters. Number of choices for the 1st letter: 26 Number of choices for the 2nd letter: 26 Number of choices for the 3rd letter: 26 Number of choices for the 4th letter: 26 Total letter combinations = 26 × 26 × 26 × 26 = 26^4 Step 3: Calculate the total number of possibilities for the digits. Number of choices for the 1st digit: 10 Number of choices for the 2nd digit: 10 Number of choices for the 3rd digit: 10 Total digit combinations = 10 × 10 × 10 = 10^3 Step 4: Multiply the possibilities for letters and digits to get the total number of different passwords. Total passwords = 26^4 × 10^3 Total passwords = 456976 × 1000 Total passwords = 456,976,000 The number of different passwords possible is 456,976,000. 2. In a group of 7 people, how many ways can a president and a vice president be selected? Step 1: Identify the type of problem. Since the positions (President and Vice President) are distinct, the order in which people are selected matters. This is a permutation problem. Step 2: Define n and k. Total number of people (n) = 7 Number of positions to fill (k) = 2 (President, Vice President) Step 3: Use the permutation formula. The formula for permutations is P(n, k) = (n!)/((n-k)!). P(7, 2) = (7!)/((7-2)!) P(7, 2) = (7!)/(5!) P(7, 2) = (7 × 6 × 5 × 4 × 3 × 2 × 1)/(5 × 4 × 3 × 2 × 1) P(7, 2) = 7 × 6 P(7, 2) = 42 Alternatively, you can think of it as: Number of choices for President: 7 people After choosing the President, number of choices for Vice President: 6 remaining people Total ways = 7 × 6 = 42 The number of ways a president and a vice president can be selected is 42.