Question

A restaurant serves custom-made omelets, where guests select meat, cheese, and vegetables to be added to their omelet. There are 6 vegetables available, and guests may select any 2 vegetables for their omelet. How many different combinations of 2 vegetables are possible?
from were get the 5 and 4

Answer 1

Answer:

15 possible combinations

Step-by-step explanation:

Given

$Vegetables = 6$

$Selection = 2$

Required

Determine the possible number of combinations

The question emphasizes on "selection" which means "combination".

So; To answer this question, we apply the following combination formula:

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

In this case:

$n = 6$

$r = 2$

The formula becomes:

$^6C_2 = \frac{6!}{(6-2)!2!}$

$^6C_2 = \frac{6!}{4!2!}$

$^6C_2 = \frac{6*5*4!}{4!2*1}$

$^6C_2 = \frac{6*5}{2}$

$^6C_2 = \frac{30}{2}$

$^6C_2 = 15$

Hence, there are 15 possible combinations