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1. Megan is in charge of creating a five-digit code to lock and unlock a secure room. She can use any digit from 0 through 9, and she can use each digit as many times as she wants. She knows she wants to start the code with a 7.

How many possible codes that start with 7 could Megan create?


10,000 codes

70,000 codes

100,000 codes

700,000 codes

2. A restaurant is serving a special lunch combo meal that includes a drink, a main dish, and a dessert. Customers can choose from 5 drinks, 6 main dishes, and 3 desserts.

How many different combo meals are possible?

Select from the drop-down menu to correctly complete the statement.

Customers can create
Choose... 14, 36, 90 or 120 different lunch combo meals.

3. Janice has room for 6 books on a shelf.

How many different ways can she arrange the books on the shelf?

Enter your answer in the box.

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By counting the numbers of options for each selection, we will see that:

  • A) There are 10,000 different codes.
  • B) There are 90 different combinations.
  • C) There are 720 different combinations.

How to get the numbers of combinations?

A) The code has five digits, and the first digit is fixed (we know that it must be 7) so we only care for the other 4.

  • The second digit has 10 possible options.
  • The third digit has 10 possible options.
  • The fourth digit has 10 possible options.
  • The fifth digit has 10 possible options.

The total number of combinations is given by the product between the numbers of combinations:

C = 1*10*10*10*10 = 10,000 codes

So the correct option is the first one.

B) Again, we need to count the number of options for each possible element.

There are 5 drinks, 6 main dishes, and 3 desserts.

So for a meal of 1 drink, 1 main dish, and 1 dessert, the total number of different combinations is:

C = 5*6*3 = 90

There are 90 different possible meals.

C) How Janice can arrange the 6 books?

We need to count how many options we have for each place on the shelf.

  • In the first place, there are 6 options (one for each book).
  • In the second place, there are 5 options (because we already placed one).
  • On the third place, there are 4 options.
  • And so on for the other 3 places.

Then the number of combinations is:

C = 6*5*4*3*2*1 = 720

There are 720 ways of ordering the books.

If you want to learn more about counting, you can read:

https://brainly.com/question/251701

Answer:

10,000

Step-by-step explanation:

Took k-12 quiz

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