A passcode to enter a building is a sequence of 444 single digit numbers (0(0left parenthesis, 0—9)9)9, right parenthesis, and repeated digits aren't allowed. Suppose someone doesn't know the passcode and randomly guesses a sequence of 444 digits. What is the probability that they guess the correct sequence? Choose 1 answer: Choose 1 answer: (Choice A) A \dfrac{1}{_{10} \, \text{P} \, _4} 10 P 4 1 start fraction, 1, divided by, start subscript, 10, end subscript, start text, P, end text, start subscript, 4, end subscript, end fraction (Choice B) B \dfrac{1}{_{10} \, \text{C} \, _4} 10 C 4 1 start fraction, 1, divided by, start subscript, 10, end subscript, start text, C, end text, start subscript, 4, end subscript, end fraction (Choice C) C \dfrac{_{4} \, \text{P} \, _4}{_{10} \, \text{P} \, _4} 10 P 4 4 P 4 start fraction, start subscript, 4, end subscript, start text, P, end text, start subscript, 4, end subscript, divided by, start subscript, 10, end subscript, start text, P, end text, start subscript, 4, end subscript, end fraction (Choice D) D \dfrac{\left(_{4} \, \text{P} \, _2\right) \cdot \left(_{4} \, \text{P} \, _2\right)}{_{10} \, \text{P} \, _4} 10 P 4 ( 4 P 2 )⋅( 4 P 2 ) start fraction, left parenthesis, start subscript, 4, end subscript, start text, P, end text, start subscript, 2, end subscript, right parenthesis, dot, left parenthesis, start subscript, 4, end subscript, start text, P, end text, start subscript, 2, end subscript, right parenthesis, divided by, start subscript, 10, end subscript, start text, P, end text, start subscript, 4, end subscript, end fraction

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07-05-2022
Mathematics

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A passcode to enter a building is a sequence of 444 single digit numbers (0(0left parenthesis, 0—9)9)9, right parenthesis, and repeated digits aren't allowed. Suppose someone doesn't know the passcode and randomly guesses a sequence of 444 digits. What is the probability that they guess the correct sequence? Choose 1 answer: Choose 1 answer: (Choice A) A \dfrac{1}{_{10} \, \text{P} \, _4} 10 P 4 1 start fraction, 1, divided by, start subscript, 10, end subscript, start text, P, end text, start subscript, 4, end subscript, end fraction (Choice B) B \dfrac{1}{_{10} \, \text{C} \, _4} 10 C 4 1 start fraction, 1, divided by, start subscript, 10, end subscript, start text, C, end text, start subscript, 4, end subscript, end fraction (Choice C) C \dfrac{_{4} \, \text{P} \, _4}{_{10} \, \text{P} \, _4} 10 P 4 4 P 4 start fraction, start subscript, 4, end subscript, start text, P, end text, start subscript, 4, end subscript, divided by, start subscript, 10, end subscript, start text, P, end text, start subscript, 4, end subscript, end fraction (Choice D) D \dfrac{\left(_{4} \, \text{P} \, _2\right) \cdot \left(_{4} \, \text{P} \, _2\right)}{_{10} \, \text{P} \, _4} 10 P 4 ( 4 P 2 )⋅( 4 P 2 ) start fraction, left parenthesis, start subscript, 4, end subscript, start text, P, end text, start subscript, 2, end subscript, right parenthesis, dot, left parenthesis, start subscript, 4, end subscript, start text, P, end text, start subscript, 2, end subscript, right parenthesis, divided by, start subscript, 10, end subscript, start text, P, end text, start subscript, 4, end subscript, end fraction

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