Suppose a traveler wanted to visit a museum, an art gallery, and the state capitol building. 45-minute tours are offered at each attraction hourly from 10 a.m. through 3 p.m. (6 different hours). Solve the problem, disregarding travel time. In how many ways could the traveler schedule all three tours before 1 p.m.?

A3
B1
C6
D9

Disregarding the time, Let's find out how many ways could the traveler schedule all three tours before 1 p.m..
Thus problem is asking "How many ways can the traveler interchange the places she wanna go.
M = museum

A = art gallery

S = state capitol

1. MAS
2. ASM
3. SAM
4. AMS
5. SMA
6. MSA

So the answer is 6.

Answer Link

AkshayG AkshayG · Answer 2 · 2019-11-19T04:46:44-05:00

The number of ways in which traveler schedule all three tours before 1 p.m. \(\boxed6\).Option (C) is correct.

Further explanation:

Given:

The options are as follows,

A. 3

B. 1

C. 6

D. 9

Calculation:

The ways in which traveler schedule all three tours before 1 p.m. can be obtained as follows,

\(\begin{aligned}{\text{Number of Ways}}&= 3!\\&= 3 \times 2 \times 1\\&= 6\\\end{aligned}\)

The ways are as follows,

1. Museum, State capitol, Art gallery.

2. Museum,Art gallery State capitol.

3. Art gallery, Museum,State capitol

4. Art gallery,State capitol,Museum

5. State capitol, Art gallery, Museum.

6. State capitol, Museum, Art gallery.

The number of ways in which traveler schedule all three tours before 1 p.m. \(\boxed6\). Option (C) is correct.

Option A is not correct.

Option B is not correct.

Option C is correct.

Option D is not correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Permutation

Keywords: Traveler, museum, an art gallery, state capital building, 45 minutes, tours, attraction hourly, disregarding travel time, traveler schedule, all three tours, before 1 pm, visit.