SOLUTION: please let me know if my answer true or false Three numbers are chosen at random without replacement from the set {0, 1, 2, 3, ... , 10}. Calculate the probabilities that for t

Question 887281: please let me know if my answer true or false
Three numbers are chosen at random without replacement from the set {0, 1, 2, 3, ... , 10}. Calculate the probabilities that for the three numbers drawn

i) None will be greater than 7,
8*7*6 / 11*10*9 = 56 / 165
ii) the smallest will be 7,
4*3*2 / 11*10*9 = 4 / 165
iii) the sum is equal to 7.
4*3*2 / 11*10*9 = 4 / 165
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p(none are greater than 7) = 8C3 / 11C3 = 56 / 165.

p(smallest will be 7) is the same as p(all are greater than or equal to 7).
4 numbers are greater than or equal to 7.
they are 7,8,9,10
p(smallest will be 7) = 4C3 / 11C3 = 4/165.

p(sum is 7)

as far as i can see, this can only be done in the following ways.

0,1,6
0,2,5
0,3,4
1,2,4

the probability is therefore 4 / 11C3 = 4/165.

i can't find anything wrong with your answers.
i couldn't really follow your formula for the last one, but the answer looks like it's what it should be.
they look good to me.

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