select the correct answer from each drop - down menu. there are 10 vehicles in a parking lot: 3 suvs and 7…

select the correct answer from each drop - down menu. there are 10 vehicles in a parking lot: 3 suvs and 7 trucks. the probability that any 7 randomly chosen parking spots have 2 suvs and 5 trucks or 3 suvs and 4 trucks is. the probability that of any 7 randomly chosen vehicles, exactly 1 is an suv is.

select the correct answer from each drop - down menu. there are 10 vehicles in a parking lot: 3 suvs and 7 trucks. the probability that any 7 randomly chosen parking spots have 2 suvs and 5 trucks or 3 suvs and 4 trucks is. the probability that of any 7 randomly chosen vehicles, exactly 1 is an suv is.

Answer

Answer:

  1. First part:
    • Calculate the number of ways to choose 7 vehicles out of 10: The formula for combinations is (C(n,r)=\frac{n!}{r!(n - r)!}), where (n = 10) and (r=7), so (C(10,7)=\frac{10!}{7!(10 - 7)!}=\frac{10!}{7!3!}=\frac{10\times9\times8}{3\times2\times1}=120).
    • Calculate the number of ways to get 2 SUVs and 5 trucks: (C(3,2)\times C(7,5)). (C(3,2)=\frac{3!}{2!(3 - 2)!}=3), (C(7,5)=\frac{7!}{5!(7 - 5)!}=\frac{7\times6}{2\times1}=21), so (C(3,2)\times C(7,5)=3\times21 = 63).
    • Calculate the number of ways to get 3 SUVs and 4 trucks: (C(3,3)\times C(7,4)). (C(3,3)=1), (C(7,4)=\frac{7!}{4!(7 - 4)!}=\frac{7\times6\times5}{3\times2\times1}=35), so (C(3,3)\times C(7,4)=1\times35 = 35).
    • The number of favorable cases for the first - part is (63 + 35=98). The probability is (\frac{98}{120}=\frac{49}{60}).
  2. Second part:
    • Calculate the number of ways to choose 1 SUV out of 3 and 6 trucks out of 7. (C(3,1)\times C(7,6)). (C(3,1)=\frac{3!}{1!(3 - 1)!}=3), (C(7,6)=\frac{7!}{6!(7 - 6)!}=7). So (C(3,1)\times C(7,6)=3\times7 = 21). The probability is (\frac{21}{120}=\frac{7}{40}).

Explanation:

Step1: Calculate total combinations

Find (C(10,7)=\frac{10!}{7!3!}=120).

Step2: Calculate combinations for 2 SUVs and 5 trucks

Find (C(3,2)\times C(7,5)), (C(3,2) = 3), (C(7,5)=21), product is 63.

Step3: Calculate combinations for 3 SUVs and 4 trucks

Find (C(3,3)\times C(7,4)), (C(3,3)=1), (C(7,4)=35), product is 35.

Step4: Calculate first - part probability

Sum favorable cases (63 + 35 = 98), probability is (\frac{98}{120}=\frac{49}{60}).

Step5: Calculate combinations for 1 SUV and 6 trucks

Find (C(3,1)\times C(7,6)), (C(3,1)=3), (C(7,6)=7), product is 21.

Step6: Calculate second - part probability

Probability is (\frac{21}{120}=\frac{7}{40}).