Probability Counting - Choose N Letters from M, Probability Counting - To nCm Notation (Level 1)

This math topic focuses on probability counting and the applications of combinatorial notation (nCm), specifically for calculating probabilities involving choosing a specific number of items from a set. It is designed to introduce students to binomial notation through problems that ask for the probability of selecting a certain number of vowels from a given set of letters, using combinations and permutations expressed in nCm notation. The problems provide various scenarios with different sets and conditions for practice.

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

Choose N Letters from M, To nCm Notation

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

What's the chance of drawing 2 vowels from this set? Show in nCm notation.

Probability Counting - Choose N Letters from M, Probability Counting - To nCm Notation Worksheet

Math worksheet on 'Probability Counting - Choose N Letters from M, Probability Counting - To nCm Notation (Level 1)'. Part of a broader unit on 'Probability and Statistics - Permutations and Combinations Calculating - Practice' Learn online: app.mobius.academy/math/units/probability_and_statistics_permutations_and_combinations_calculation_practice/

An svg image showing a math problem

What's the chance of drawing 2 vowels from this set? Show in nCm notation.

a $A LaTex expression showing \frac{ sub 3 \text{B} sub 2 }{ sub 7 \text{P} sub 2 }$

b $A LaTex expression showing \frac{ sub 3 \text{C} sub 2 }{ sub 7 \text{C} sub 2 }$

c $A LaTex expression showing \frac{ sub 3 \text{R} sub 2 }{ sub 8 \text{C} sub 3 }$

d $A LaTex expression showing \frac{ sub 3 \text{P} sub 2 }{ sub 2 \text{C} sub 7 }$

e $A LaTex expression showing \frac{ sub 4 \text{C} sub 4 }{ sub 7 \text{P} sub 2 }$

f $A LaTex expression showing \frac{ sub 3 \text{C} sub 2 }{ sub 7 \text{R} sub 2 }$

An svg image showing a math problem

What's the chance of drawing 2 vowels from this set? Show in nCm notation.

a $A LaTex expression showing \frac{ sub 3 \text{P} sub 2 }{ sub 6 \text{R} sub 2 }$

b $A LaTex expression showing \frac{ sub 3 \text{P} sub 2 }{ sub 6 \text{B} sub 2 }$

c $A LaTex expression showing \frac{ sub 3 \text{P} sub 2 }{ sub 6 \text{P} sub 2 }$

d $A LaTex expression showing \frac{ sub 3 \text{C} sub 2 }{ sub 6 \text{R} sub 2 }$

e $A LaTex expression showing \frac{ sub 3 \text{C} sub 2 }{ sub 6 \text{C} sub 2 }$

f $A LaTex expression showing \frac{ sub 2 \text{C} sub 3 }{ sub 6 \text{R} sub 2 }$

An svg image showing a math problem

What's the chance of drawing 3 vowels from this set? Show in nCm notation.

a $A LaTex expression showing \frac{ sub 3 \text{C} sub 4 }{ sub 7 \text{R} sub 3 }$

b $A LaTex expression showing \frac{ sub 4 \text{C} sub 2 }{ sub 3 \text{C} sub 7 }$

c $A LaTex expression showing \frac{ sub 4 \text{C} sub 3 }{ sub 7 \text{C} sub 3 }$

d $A LaTex expression showing \frac{ sub 4 \text{P} sub 3 }{ sub 7 \text{P} sub 3 }$

e $A LaTex expression showing \frac{ sub 4 \text{P} sub 3 }{ sub 3 \text{C} sub 7 }$

f $A LaTex expression showing \frac{ sub 4 \text{P} sub 3 }{ sub 7 \text{C} sub 2 }$

An svg image showing a math problem

What's the chance of drawing 2 vowels from this set? Show in nCm notation.

a $A LaTex expression showing \frac{ sub 3 \text{R} sub 2 }{ sub 6 \text{P} sub 2 }$

b $A LaTex expression showing \frac{ sub 3 \text{P} sub 2 }{ sub 4 \text{C} sub 4 }$

c $A LaTex expression showing \frac{ sub 3 \text{R} sub 2 }{ sub 2 \text{C} sub 6 }$

d $A LaTex expression showing \frac{ sub 3 \text{R} sub 2 }{ sub 8 \text{C} sub 3 }$

e $A LaTex expression showing \frac{ sub 3 \text{C} sub 2 }{ sub 6 \text{P} sub 2 }$

f $A LaTex expression showing \frac{ sub 3 \text{C} sub 2 }{ sub 6 \text{C} sub 2 }$

An svg image showing a math problem

What's the chance of drawing 2 vowels from this set? Show in nCm notation.

a $A LaTex expression showing \frac{ sub 4 \text{P} sub 2 }{ sub 5 \text{P} sub 2 }$

b $A LaTex expression showing \frac{ sub 5 \text{C} sub 4 }{ sub 2 \text{C} sub 5 }$

c $A LaTex expression showing \frac{ sub 2 \text{C} sub 4 }{ sub 7 \text{C} sub 4 }$

d $A LaTex expression showing \frac{ sub 4 \text{P} sub 2 }{ sub 2 \text{C} sub 5 }$

e $A LaTex expression showing \frac{ sub 4 \text{B} sub 2 }{ sub 5 \text{P} sub 2 }$

f $A LaTex expression showing \frac{ sub 4 \text{C} sub 2 }{ sub 5 \text{C} sub 2 }$

An svg image showing a math problem

What's the chance of drawing 2 vowels from this set? Show in nCm notation.

a $A LaTex expression showing \frac{ sub 4 \text{C} sub 2 }{ sub 5 \text{C} sub 2 }$

b $A LaTex expression showing \frac{ sub 4 \text{P} sub 2 }{ sub 5 \text{P} sub 2 }$

c $A LaTex expression showing \frac{ sub 4 \text{P} sub 2 }{ sub 5 \text{R} sub 2 }$

d $A LaTex expression showing \frac{ sub 4 \text{B} sub 2 }{ sub 5 \text{B} sub 2 }$

e $A LaTex expression showing \frac{ sub 4 \text{R} sub 2 }{ sub 2 \text{C} sub 5 }$

f $A LaTex expression showing \frac{ sub 4 \text{P} sub 2 }{ sub 5 \text{C} sub 3 }$

An svg image showing a math problem

What's the chance of drawing 3 vowels from this set? Show in nCm notation.

a $A LaTex expression showing \frac{ sub 4 \text{C} sub 3 }{ sub 6 \text{C} sub 3 }$

b $A LaTex expression showing \frac{ sub 3 \text{C} sub 3 }{ sub 8 \text{C} sub 4 }$

c $A LaTex expression showing \frac{ sub 4 \text{B} sub 3 }{ sub 6 \text{P} sub 3 }$

d $A LaTex expression showing \frac{ sub 4 \text{P} sub 3 }{ sub 7 \text{C} sub 5 }$

e $A LaTex expression showing \frac{ sub 4 \text{P} sub 3 }{ sub 4 \text{C} sub 3 }$

f $A LaTex expression showing \frac{ sub 4 \text{P} sub 3 }{ sub 6 \text{P} sub 3 }$