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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. 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?
Expert Solution
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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