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A 6-digit code is to be created with no repeating digits, where the first digit is fixed as 4 and the last digit is fixed as 7. How many unique codes can be formed?
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Solution: Step 1: Fix first digit as 4 and last digit as 7 Step 2: Remaining 4 digits to be filled from 8 available digits (0, 1, 2, 3, 5, 6, 8, 9) Step 3: Number of permutations for 4 digits from 8 = 8 × 7 × 6 × 5 Step 4: Calculate: 8 × 7 = 56 Step 5: 56 × 6 = 336 Step 6: 336 × 5 = 1680 Step 7: Total unique codes = 1680
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