Answered

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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

Sagot :

MrRoyal

Answer:

15 possible combinations

Step-by-step explanation:

Given

[tex]Vegetables = 6[/tex]

[tex]Selection = 2[/tex]

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:

[tex]^nC_r = \frac{n!}{(n-r)r!}[/tex]

In this case:

[tex]n = 6[/tex]

[tex]r = 2[/tex]

The formula becomes:

[tex]^6C_2 = \frac{6!}{(6-2)!2!}[/tex]

[tex]^6C_2 = \frac{6!}{4!2!}[/tex]

[tex]^6C_2 = \frac{6*5*4!}{4!2*1}[/tex]

[tex]^6C_2 = \frac{6*5}{2}[/tex]

[tex]^6C_2 = \frac{30}{2}[/tex]

[tex]^6C_2 = 15[/tex]

Hence, there are 15 possible combinations

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