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Tycho wants to prepare a schedule for his exercise over the next few months. Every week, he wants to exercise on the same days of the week. He does not want to exercise on two consecutive days. He wants to exercise three days per week. How many schedules can he choose from?

A. 6
B. 7
C. 9
D. 10
E. 35

Answer :

There are a total of 9 possible schedules that Tycho can choose from.

Thus, option (C) is correct.

Let consider the days of the week as Monday (M), Tuesday (T), Wednesday (W), Thursday (Th), Friday (F), Saturday (Sa), and Sunday (Su).

To create a schedule for exercise, Tycho needs to choose three days of the week to exercise such that no two exercise days are consecutive.

So, the possibilities are:

1. Tycho chooses Monday, Wednesday, and Friday.

The schedule is MW FSu.

2. Tycho chooses Monday, Wednesday, and Saturday.

The schedule is MW SaSu.

3. Tycho chooses Monday, Thursday, and Saturday.

The schedule is MT F SaSu.

4. Tycho chooses Monday, Thursday, and Sunday.

The schedule is MT SaSu.

5. Tycho chooses Tuesday, Thursday, and Saturday.

The schedule is TThSaSu.

6. Tycho chooses Tuesday, Thursday, and Sunday.

The schedule is TTSaSu.

7. Tycho chooses Tuesday, Friday, and Sunday.

The schedule is TFSaSu.

8. Tycho chooses Wednesday, Friday, and Sunday.

The schedule is W F SaSu.

9. Tycho chooses Wednesday, Thursday, and Saturday.

The schedule is W T FSaSu.

Thus, total of 9 possible schedules that Tycho can choose from.

Thus, option (C) is correct.

Learn more about Combination here:

https://brainly.com/question/29595163

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