Choose N Letters from M, Count of Favorable Outcomes - To Factorial Equation (Level 1)

This math topic focuses on calculating probabilities using combinatorial arguments, specifically emphasizing the selection of a subset of items (e.g., vowels) from a larger set, expressed in factorial notation. The problems involve determining the number of favorable outcomes for selecting a specific number of items from the set and require applying permutations and combinations formulas. The skills practiced include understanding factorial calculations, combinations, and the binomial coefficient within the broader framework of introductory probability and statistics.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Probability Counting - Choose N Letters from M, Count of Favorable Outcomes - To Factorial Equation Worksheet

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Probability Counting - Choose N Letters from M, Count of Favorable Outcomes - To Factorial Equation
1
An svg image showing a math problem
How many ways can 2 vowels be drawn from this set? Show as a factorial.
a A LaTex expression showing 2! over 3! times 1!
b A LaTex expression showing 3!
c A LaTex expression showing 3! over 2! times 1!
d A LaTex expression showing 4! over 2! times 2!
2
An svg image showing a math problem
How many ways can 2 vowels be drawn from this set? Show as a factorial.
a A LaTex expression showing 3! over 2! times 1!
b A LaTex expression showing 2! over 3! times 1!
c A LaTex expression showing 5! over 3! times 2!
d A LaTex expression showing 4! over 3! times 1!
e A LaTex expression showing 3!
3
An svg image showing a math problem
How many ways can 3 vowels be drawn from this set? Show as a factorial.
a A LaTex expression showing 6! over 3! times 3!
b A LaTex expression showing 4!
c A LaTex expression showing 3! over 4! times 1!
d A LaTex expression showing 4! over 3! times 1!
e A LaTex expression showing 3! over 3! times 0!
4
An svg image showing a math problem
How many ways can 3 vowels be drawn from this set? Show as a factorial.
a A LaTex expression showing 4! over 3! times 1!
b A LaTex expression showing 4! over 2! times 2!
c A LaTex expression showing 3! over 4! times 1!
d A LaTex expression showing 4!
5
An svg image showing a math problem
How many ways can 3 vowels be drawn from this set? Show as a factorial.
a A LaTex expression showing 4! over 2! times 2!
b A LaTex expression showing 3! over 4! times 1!
c A LaTex expression showing 4! over 3! times 1!
d A LaTex expression showing 3! over 3! times 0!
e A LaTex expression showing 4!
6
An svg image showing a math problem
How many ways can 3 vowels be drawn from this set? Show as a factorial.
a A LaTex expression showing 4!
b A LaTex expression showing 5! over 3! times 2!
c A LaTex expression showing 4! over 3! times 1!
d A LaTex expression showing 3! over 4! times 1!
7
An svg image showing a math problem
How many ways can 2 vowels be drawn from this set? Show as a factorial.
a A LaTex expression showing 3!
b A LaTex expression showing 3! over 2! times 1!
c A LaTex expression showing 4! over 4! times 0!
d A LaTex expression showing 2! over 3! times 1!
8
An svg image showing a math problem
How many ways can 2 vowels be drawn from this set? Show as a factorial.
a A LaTex expression showing 2! over 4! times 2!
b A LaTex expression showing 4! over 2!
c A LaTex expression showing 4! over 2! times 2!