Question

A college needs two additional faculty members: a chemist and a statistician. In how many ways can these positions be filled if there are five applicants for the chemistry position and three applicants for the statistics position?

Answer 1

Answer:

15 ways.  

Step-by-step explanation:

We have been given that a college needs two additional faculty members. We are asked to find the number of ways in which these positions can be filled if there are five applicants for the chemistry position and three applicants for the statistics position.

We will use combinations for solve our given problem.    

$^nC_r=\frac{n!}{r!(n-r)!}$, where,

n = Number of total items,

r = Items being chosen at a time.

$^5C_1\cdot ^3C_1=\frac{5!}{1!(5-1)!}\cdot \frac{3!}{1!(3-1)!}$

$^5C_1\cdot ^3C_1=\frac{5!}{1!(4)!}\cdot \frac{3!}{1!(2)!}$

$^5C_1\cdot ^3C_1=\frac{5*4!}{1*4!}\cdot \frac{3*2!}{1*2!}$

$^5C_1\cdot ^3C_1=5\cdot 3$

$^5C_1\cdot ^3C_1=15$

Therefore, the positions can be filled in 15 ways.