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


(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}timesfrac{1}{7}timesfrac{1}{6}=frac{1}{336}