Question

A travel company had a contest, and Bree won a trip to seven countries. The rules are that Bree mist visit the countries in the order told to her by the travel company, but she can decide to skip visiting any of the countries except the first one. So, Bree can visit a total of 1,2,3,4,5,6 or 7 countries. In how many ways can Bree organize her trip?

QUICK I NEED HELP AS SOON AS POSSIBLE

Answer 1

64

Explanation:

You want to know the number of ways Bree can choose to visit any or all of the remaining 6 countries on a trip to (possibly) seven countries when the order is specified.

Choices

Bree's itinerary will be of the form ...

• country 1
• country 2 – or not
• country 3 – or not
• country 4 – or not
• ...
• country 7 – or not

At each point in Bree's trip, she can make a choice to visit the country, or not. That is, there are 2 possibilities of outcome for each of 6 choices.

The total number of possibilities is ...

1 × 2 × 2 × 2 × 2 × 2 × 2 = 64

Bree can organize her trip in any of 64 different ways.

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