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Rosa's friend Jake claims that he can read minds. To test Jake's abilities, Rosa chooses 3 different numbers from 1 to 10 . Rosa then asks Jake to identify which 3 of the 10 numbers she chose in the correct order. Assume that Jake has no special abilities and is randomly guessing the numbers. What is the probability that Jake correctly identifies all 3 numbers in the correct order? Choose 1 answer: (A) (1)/(120) (B) (1)/(420) (C) (1)/(720) (D) (1)/(5,040)

Rosa's friend Jake claims that he can read minds. To test Jake's abilities, Rosa chooses 33 different numbers from 11 to 1010 . Rosa then asks Jake to identify which 33 of the 1010 numbers she chose in the correct order.\newlineAssume that Jake has no special abilities and is randomly guessing the numbers.\newlineWhat is the probability that Jake correctly identifies all 33 numbers in the correct order?\newlineChoose 11 answer:\newline(A) 1120 \frac{1}{120} \newline(B) 1420 \frac{1}{420} \newline(C) 1720 \frac{1}{720} \newline(D) 15,040 \frac{1}{5,040}

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Q. Rosa's friend Jake claims that he can read minds. To test Jake's abilities, Rosa chooses 33 different numbers from 11 to 1010 . Rosa then asks Jake to identify which 33 of the 1010 numbers she chose in the correct order.\newlineAssume that Jake has no special abilities and is randomly guessing the numbers.\newlineWhat is the probability that Jake correctly identifies all 33 numbers in the correct order?\newlineChoose 11 answer:\newline(A) 1120 \frac{1}{120} \newline(B) 1420 \frac{1}{420} \newline(C) 1720 \frac{1}{720} \newline(D) 15,040 \frac{1}{5,040}
  1. Calculate Permutations: To solve this problem, we need to calculate the probability of Jake guessing the correct numbers in the correct order. Since Jake is guessing, each number he picks is independent of the previous one. The total number of ways to choose 33 numbers from 1010 is the number of permutations of 1010 items taken 33 at a time.\newlineThe formula for permutations is P(n,k)=n!(n−k)!P(n, k) = \frac{n!}{(n - k)!}, where nn is the total number of items to choose from, and kk is the number of items to choose.
  2. Total Permutations: First, we calculate the total number of permutations for choosing 33 numbers out of 1010.\newlineP(10,3)=10!(10−3)!=10!7!=10×9×8=720P(10, 3) = \frac{10!}{(10 - 3)!} = \frac{10!}{7!} = 10 \times 9 \times 8 = 720.\newlineThis is the total number of ways Jake can guess 33 numbers in order.
  3. Calculate Probability: Since Jake is guessing, there is only 11 correct order out of these 720720 possibilities. Therefore, the probability that Jake guesses correctly is 11 divided by the total number of permutations.\newlineThe probability is P=1720P = \frac{1}{720}.
  4. Match with Choices: We can now match our calculated probability with the given choices.\newlineThe correct probability is (1)/(720)(1)/(720), which corresponds to choice (C).

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