Question

**three students decide to go sailing. Upon arriving at
the boat however, they discover that it is too dark below decks to
clearly see the sails. Knowing that there are 3 jibs, 5 mains and 2
spinnakers on board, if each student goes below once and returns
with a randomly picked sail, what is the probability that 2 or
fewer jibs will end up above decks ?**

**without replacement**

**i started doing it like this: p(j**≤3)=1 p(j≤2) +
p(j=3)

p(j≤2)=1-p(j=3)

Answer #1

Probability that 2 or fewer jibs will end up above decks = Probability that at least one jib is picked by three students

= 1 - Probability that no jibs are picked by three students

= 1 - Probability that no jibs are picked by 1st student * Probability that no jibs are picked by 2nd student * Probability that no jibs are picked by 3rd student

= 1 - (7/10) * (6/ 9) * (5/ 8) (For 1st student, there are 3 jibs and 7 non-jibs. For 2nd student when mains or spinnaker is picked, there are 3 jibs and 6 non-jibs. For 3rd student when another mains or spinnaker is picked, there are 3 jibs and 5 non-jibs. )

= 1 - 7/24

= 17/24

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