Question

Boeing currently produces five models of airplanes for commercial sale. The airline that Lauren works for is rapidly expanding and would like to purchase three airplanes of different models to service various routes. Her job is to analyze which three to buy. How many combinations will she have to analyze

Answer 1

Answer:

10 combinations

Step-by-step explanation:

Given

$n = 5$ --- total production

$r = 3$ --- aircraft to select

Required

The total number of combination

The number of combination is calculated using:

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

So, we have:

$^5C_3 = \frac{5!}{(5 - 3)!*3!}$

$^5C_3 = \frac{5!}{2!*3!}$

Expand

$^5C_3 = \frac{5*4*3!}{2*1*3!}$

$^5C_3 = \frac{5*4}{2*1}$

$^5C_3 = \frac{20}{2}$

$^5C_3 = 10$