Hanson is planning a trip to South America. He has a list of 4 countries he would like to see, but doesn't have time to visit all of them. He asks a travel agent to make an itinerary that includes any 2 of the 4 countries. How many sequences of 2 countries are possible?​

Respuesta :

There are 6 ways of the sequence of the 2 countries from the combination.

According to the statement

We have to find the possible number of the sequence with the given information.

So, For this purpose, we know that the

From given information:

He has a list of 4 countries and He asks a travel agent to make an itinerary that includes any 2 of the 4 countries.

here to find the sequence we use the combination here

Combination is the number of possible arrangements in a collection of items where the order does not matter.

The formula to calculate combination is

[tex]C_{r} ^{n}[/tex]

According to the information the combination become of 4 and 2.

So,

[tex]C_{2} ^{4} = \frac{4!}{2! * 2!}[/tex]

[tex]C_{2} ^{4} = \frac{4*3*2*1}{2*1 * 2*1}[/tex]

[tex]C_{2} ^{4} = 6[/tex].

There are 6 ways by the combination.

So, There are 6 ways of the sequence of the 2 countries from the combination.

Learn more about Combination here

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