Bunuel wrote:
GRE Multiple Answer Challenge Question
A space program is recruiting a team of astronauts to journey to Mars aboard a four-person shuttle. If the number of possible teams is less than 100 but greater than 10, then what is the possible number of astronauts who did not make the space team? Indicate all such numbers.
[A] 9
8
[C] 7
[D] 6
[E] 5
[F] 4
[G] 3
[H] 2
[I] 1
Kudos for correct solution.[b]So, the question is about possible number of teams, thus a combination problem--- nCr
In nCr, r is 4, so nC4..
What is n? -
It is given in the choices, that is CHOICE + 4so (9+4)C4, (8+4)C4, (7+4)C4,....(2+4)C4, (1+4)C4..
Also \(10<nC4<100\)...
1) \(nC4>10\)
Take n as the least (1+4) so 5C4=5, which is less than 10, so take next higher
take n as the 6,so \(6C4 = \frac{6*5}{2}=15\), greater than 10.. so possible
2)\(nC4<100\)
take n as 13, \(13C4 = \frac{13*12*11*10}{4*3*2}=715\), way more than 100 so take the middle value in the choice
n =9, so \(9C4 = \frac{9*8*7*6}{4*3*2}=126\), so >100
n=8, so \(8C4 = \frac{8*7*6*5}{4*3*2}=70\)
so n is from 6 to 8
if 4 are sent, the number of astronaut left can be (6-4), (7-4) or (8-4), thus 2, 3, or 4