Question

There are 15 research doctors participating in the study and the research board needs to be established with the offices of director, assistant director, quality control analyst, and correspondent. (Doctors can only hold one office on the research board.) Determine how many ways this research board can be chosen and explain your process.

Answer 1

Answer: There are 32,760 ways that research board can be chosen.

Step-by-step explanation:

Since we have given that

Number of research doctors participating in the study = 15

the research board requires to be established with offices of director, Assistant director, Quality control analyst, and Correspondent.

Since there are 15 choices for the Offices of director,

There are 14 choices for the Assistant director,

There are 13 choices for Quality control analyst,

There are 12 choices for Correspondent.

So, by applying "Fundamental theorem of counting", we get that

Number of ways that research board can be chosen is given by

$15\times 14\times 13\times 12\\\\=32,760$

Hence, there are 32,760 ways that research board can be chosen.

Answer 2

Answer:

32760

Step-by-step explanation:

There are 4 positions on the board.  There are 15 possible candidates for the first position.  That leaves 14 candidates for the second position.  Which leaves 13 for the third position, and 12 for the fourth position.

15 × 14 × 13 × 12 = 32760