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Let a be the number of permutations of x + 2 objects taken all at once, b be the number of permutations of x objects taken 11 at a time, and c be the number of permutations of x − 11 objects taken all at once. If a = 182bc, then what is the value of x?
- 12
- 10
- 8
- 6
Correct answer: 12
Solution
The equation a = 182bc relates the permutations of different sets of objects. By substituting the formulas for permutations, we can solve for x, and through calculations, we find that x must equal 12 to satisfy the equation.
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