From a group of 21 astronauts that includes 12 people with

BTGmoderatorLU wrote:Source: GMAT Prep

From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly one person in the crew has previous experience in space flight. How many different crews of this type are possible?

A. 432
B. 94
C. 864
D. 1330
E. 7980

$$21\,\,{\rm{astron}}\,\,\,\left\{ \matrix{
\,12\,\,{\rm{experts}} \hfill \cr
\,21 - 12 = 9\,\,{\rm{non}}\,{\rm{experts}} \hfill \cr} \right.$$
$$?\,\,\, = \,\,\,\,\# \,\,3\,{\text{people - group}}\,\,,\,\,{\text{exactly}}\,\,1\,\,{\text{expert}}$$
$$?\,\,\, = \,\,\,12 \cdot C\left( {9,2} \right)\,\,\, = 12 \cdot \frac{{9 \cdot 8}}{2} = \underleftrightarrow {9 \cdot 48\,\, = \,\,360 + 72}\,\,\, = \,\,\,432$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.