Probability Counting - Choose N Cards from M, Count of Favorable Outcomes - To nCm Notation (Level 1) - Mobius Math Academy

Probability Counting

Choose N Cards from M, Count of Favorable Outcomes - To nCm Notation (Level 1)

This math topic focuses on probability counting involving the selection of cards from a set, specifically calculating the number of favorable outcomes using binomial coefficients, denoted by nCm notation. Each problem presents a scenario where learners need to determine how many ways specific cards, such as tens, kings, fives, or jacks, can be drawn from different card sets. The correct representation of these calculations in nCm form is then assessed through multiple choice answers, also given in nCm and related notations. It combines practical application of probability with an introduction to binomial expressions.

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

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Probability Counting - Choose N Cards from M, Count of Favorable Outcomes - To nCm Notation Worksheet

Probability Counting - Choose N Cards from M, Count of Favorable Outcomes - To nCm Notation

An svg image showing a math problem

How many ways can two 4s be drawn from this set? Show in nCm notation.

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

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

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

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

e $A LaTex expression showing sub 3 \text{R} sub 2$

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

An svg image showing a math problem

How many ways can two 9s be drawn from this set? Show in nCm notation.

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

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

c $A LaTex expression showing sub 5 \text{C} sub 2$

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

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

f $A LaTex expression showing sub 4 \text{R} sub 2$

An svg image showing a math problem

How many ways can two 5s be drawn from this set? Show in nCm notation.

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

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

c $A LaTex expression showing sub 4 \text{B} sub 2$

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

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

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

An svg image showing a math problem

How many ways can two Jacks be drawn from this set? Show in nCm notation.

a $A LaTex expression showing sub 4 \text{B} sub 2$

b $A LaTex expression showing sub 4 \text{R} sub 2$

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

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

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

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

An svg image showing a math problem

How many ways can two Queens be drawn from this set? Show in nCm notation.

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

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

c $A LaTex expression showing sub 3 \text{B} sub 2$

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

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

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

An svg image showing a math problem

How many ways can three Kings be drawn from this set? Show in nCm notation.

a $A LaTex expression showing sub 4 \text{P} sub 3$

b $A LaTex expression showing sub 4 \text{B} sub 3$

c $A LaTex expression showing sub 4 \text{R} sub 3$

d $A LaTex expression showing sub 4 \text{C} sub 3$

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

f $A LaTex expression showing sub 3 \text{C} sub 4$

An svg image showing a math problem

How many ways can three Queens be drawn from this set? Show in nCm notation.

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

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

c $A LaTex expression showing sub 4 \text{R} sub 3$

d $A LaTex expression showing sub 4 \text{B} sub 3$

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

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

An svg image showing a math problem

How many ways can two 4s be drawn from this set? Show in nCm notation.

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

b $A LaTex expression showing sub 4 \text{B} sub 2$

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

d $A LaTex expression showing sub 4 \text{R} sub 2$

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

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