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A standard deck of playing cards has 52 cards: 13 spades, 13 clubs, 13 hearts, and 13 diamonds. What is the probability of drawing a spade from a standard 52 -card deck, replacing it, and then drawing another spade? Show your work or explain how you got your answer.
Using the letters in the word FABRIC, find the number of permutations that can be formed using 2 letters at a time. Show your work or explain how you got your answer.
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Step 1I'll solve both problems step by step, following the specified LaTeX formatting guidelines:
Problem 1: Probability of Drawing Spades
Step 2: Determine the number of spades in a standard deck
- Total spades = $$13$$ cards
- Total cards in deck = 52 cards
Final Answer
Problem 2: Permutations of FABRIC Step 1: Count the number of unique letters in FABRIC - Unique letters: F, A, B, R, I, C - Total unique letters = 6 Step 2: Calculate permutations using the permutation formula - We want to select 2 letters at a time - Formula: P(n,r) = \frac{n!}{(n-r)!} - Here, n = 6, r = 2 Step 3: Apply the permutation formula P(6,2) = \frac{6!}{(6 - 2)!} = \frac{6!}{4!} Step 4: Calculate the result \frac{6!}{4!} = \frac{6 \times 5 \times 4!}{4!} = 6 \times 5 = 30
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