This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems: 5. In a deck of 52 cards, how many ways can you draw 2 cards without replacement? Step 1: Identify the type of problem. We are selecting 2 cards from 52 without replacement. The phrasing "how many ways can you draw 2 cards" can be interpreted in two ways: If the order of drawing the cards does not matter (e.g., drawing King of Hearts then Queen of Spades is the same as drawing Queen of Spades then King of Hearts), it's a combination problem. If the order of drawing the cards does matter, it's a permutation problem. Step 2: Calculate combinations and permutations. Number of combinations C(n, k) = (n!)/(k!(n-k)!): C(52, 2) = (52!)/(2!(52-2)!) = (52!)/(2!50!) = (52 × 51)/(2 × 1) = 26 × 51 = 1326 Number of permutations P(n, k) = (n!)/((n-k)!): P(52, 2) = (52!)/((52-2)!) = (52!)/(50!) = 52 × 51 = 2652 Step 3: Compare with the given options. The options are a) 102, b) 2652, c) 132, d) 263. The combination result (1326) is not among the options. The permutation result (2652) matches option b). Given that 2652 is an option