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1.There are 10 kids running a race. How many ways are there for them to come in first, second, and third place?


2.In a drawing, a jar holds the numbers 1 to 8. If you draw three numbers to form a three-digit number (without replacement), what is the probability you will draw 135?

Verified Answer :

HomertheGenius
  1. 10 x 9 x 8 = 720
    There are 720 ways for them to come in first, second and third place.
    2. Probability = 1/8 x 1/7 x 1/6 = 1/336
    The probability is 1/336 or 0.002976.

Answer:

1: 720

2: \(\frac{1}{336}\)

Step-by-step explanation:

1: There are 10 kids in a race so the number of ways such that they come first , second and third=10×9×8

                           =720

(since the first place is occupied by any one of the ten students i.e. we have ten choices after occupying first position there are only 9 students left for second position and after occupying second for the third position only 8 choices are left)

2: We have to find the probability such that there is no replacement  such that we draw 135.

for the first position we have to find the probability(\(P_{1}\)) that '1' comes out of 8 numbers=\(\frac{1}{8}\)

similarly for second choice we could not take 1 as there is no replacement

so probability that 3 comes(\(P_{2}\)) =\(\frac{1}{7}\)

similarly probability that 5 comes at third position(\(P_{3}\)) = \(\frac{1}{6}\)

hence, probability that 135 is drawn= \(\frac{1}{8}\times\frac{1}{7}\times\frac{1}{6}=\frac{1}{336}\)


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