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Homework answers / question archive / In how many ways can 7 instructors be assigned to seven sections of a course in mathematics? How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview? A man has 8 pairs of pants, 5 shirts, and 3 ties

In how many ways can 7 instructors be assigned to seven sections of a course in mathematics? How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview? A man has 8 pairs of pants, 5 shirts, and 3 ties

Math

In how many ways can 7 instructors be assigned to seven sections of a course in mathematics?

How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview?

A man has 8 pairs of pants, 5 shirts, and 3 ties. How many different outfits can he wear?

Two balls are to be selected without replacement from a bag containing one red, one blue, one green, one yellow, and one black ball. How many points are there in the sample space?

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please see the attached file for detailed solution.

1. This is a permutation problem
P(7, 7) = 7! = 5040
So there are 5040 ways.

2. The is a combination problem
19C7 = 19! /7! / (19-7)! = 50388

3. There are 8 ways to choose the pants, 5 ways to choose a shirt, and 3 ways to choose a tie.
8C1 * 5C1 * 3C1 = 8 * 5 * 3 = 120

4. Selection without replacement of 2 from 5 unique colors, where order is unimportant.
5C2 = 5* 4 / 2! = 10
There are 10 points in the sample space.

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