From a class of 28 students, in how many ways could a teacher select 4 students to lead the class discussion?
Table of contents
- 0. Review of Algebra4h 18m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations1h 43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 5m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 22m
- 10. Combinatorics & Probability1h 45m
10. Combinatorics & Probability
Combinatorics
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Phone numbers are 10 digits long. How many possible phone numbers are there if the 1st and 4th numbers can't be 0?
A
10
B
90
C
8,100,000,000
D
10,000,000,000

1
Understand that a phone number is a sequence of 10 digits, where each digit can range from 0 to 9.
Identify the constraints: the 1st and 4th digits cannot be 0, meaning they can be any digit from 1 to 9.
Calculate the number of choices for the 1st digit: since it cannot be 0, there are 9 possible choices (1-9).
Calculate the number of choices for the 4th digit: similarly, there are 9 possible choices (1-9).
Calculate the number of choices for the remaining 8 digits: each can be any digit from 0 to 9, giving 10 choices per digit. Multiply the choices for each digit to find the total number of possible phone numbers.
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