The fire chief is throwing a Christmas party for
the 24 firefighters, medics, and officers in her
volunteer fire department. She finds 6 different
Disney characters dressed in protective bunker
gear and buys an equal number of each. All
packages are wrapped the same way and each
member of the department selects his or her own
gift. The medical officer selects first, followed by
the engineer and then the deputy chief. What is
the probability that each of the three will select the
Pooh Bear character?
A 5/506
B 1/506
C 5/576
D 1/576

Question

The fire chief is throwing a Christmas party for
the 24 firefighters, medics, and officers in her
volunteer fire department. She finds 6 different
Disney characters dressed in protective bunker
gear and buys an equal number of each. All
packages are wrapped the same way and each
member of the department selects his or her own
gift. The medical officer selects first, followed by
the engineer and then the deputy chief. What is
the probability that each of the three will select the
Pooh Bear character?
A 5/506
B 1/506
C 5/576
D 1/576

mathmate · Answer

24 members in the department, 6 types of gears, so 4 of each kind.
Medical officer chooses 4 Pooh Bear character out of 24, with probability 4/24.
Engineer chooses remaining 3 out of 23, with probability of 3/23
Deputy chief chooses 2 remaining out of 22, with probability of 2/22

For all of this to happen, we multiply the individual probabilities, so
P(all Pooh Bears) = (4/24)*(3/23)*(2/22)=1/506