Discrete Probability Distribution

from walpole 5.32

From a lot of 10 missiles, 4 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that

a) all 4 will fire

b) at most 2 will not fire ?

I believe this is a hypergeometric distribution.

pls correct me if i am wrong.

a) since all 4 , i took P(x= 0) + .....P(x=4)

4C0 x 6C4 / 10C4 + 4C1 x 6C3 / 10C4 + .....

and i got 13/14. but this does not tally with the answer stated on my worksheet. where did i go wrong ?

b) at most 2 will not fire means P (X<=2) ?