Question

A twenty-something single person is planning a ski vacation. Assume that she has 3 possible destinations: New England, Utah, and Oregon. There are 3 ski areas in New England with 2 available times for 2 of the areas, and 3 times for the other area. There are 4 ski areas in Utah with 4 available times for 3 of the areas, and 3 times for the other area. There are 4 ski areas in Oregon with 4 available times for 3 of the areas, and 3 times for the other area. (A "time" refers to a weekend for which there are vacancies at the ski lodge.) A trip plan involves the selection of a location, ski area, and a time.How many possible plans are there?

Answer 1

Number of a trip plans:
1 ) New England: 2 * 2 + 1 * 3 = 4 + 3 = 7
2 ) Utah: 3 * 4 + 1 * 3 = 12 + 3 = 15
3 ) Oregon: 3 * 4 + 1 * 3 = 12 + 3 = 15
In total: 7 + 15 + 15 = 37
Answer: There are 37 possible trip plans.

Answer 2

Possible number of plans are 37.

Explanation:

To find : How many possible plans are there?

Given : Assume that she has 3 possible destinations: New England, Utah, and Oregon.

There are 3 ski areas in New England with 2 available times for 2 of the areas, and 3 times for the other area.

Number of trips plan in New England is

2 available times for 2 of the areas =
`2* 2=4`

3 times for the other area =
`3* 1=3`

Total = 4+3=7

There are 4 ski areas in Utah with 4 available times for 3 of the areas, and 3 times for the other area.

Number of trips plan in Utah is

4 available times for 3 of the areas =
`4* 3=12`

3 times for the other area =
`3* 1=3`

Total = 12+3=15

There are 4 ski areas in Oregon with 4 available times for 3 of the areas, and 3 times for the other area.

Number of trips plan in Oregon is

4 available times for 3 of the areas =
`4* 3=12`

3 times for the other area =
`3* 1=3`

Total = 12+3=15

Total number of trip plans : 7+ 15 + 15 = 37

Therefore, possible number of plans are 37.