n Pr 
nCr 
Probabilities with Counting Techniques
Selecting r items from a total of n items where there is a certain order
Selecting r items from a total of n items where there can be any order
The Probability that your defined event A will occur
n( A)
P( A) 
n( S )
n(A) = the total number of outcomes in which event A can occur
n(S) = the total number of possible outcomes
1.
You are swimming in a race and have drawn the middle lane. What is the probability that the two fastest
swimmers are beside you in the race if there are 6 lanes occupied?
2.
Jon, Jordon, Justin are running for President and Scott, Zack, Wade and Matt are running for Vice President of
the Poker Club. What is the probability that:
a) Justin will be elected President?
b) Matt will be Vice President?
c)
Justin and Matt will be elected to their positions?
d) Justin or Matt or Both will be elected to their positions?
3.
What is the probability of drawing 2 Aces from a deck of cards if the cards are drawn:
a) With replacement?
b) Without replacement?
4.
What is the probability of a 5 card poker hand with 2 Jacks and 2 Kings?
5.
What is the probability of a 5 card poker hand with a pair and three of a kind (this is called a full house)?
6.
What is the probability of a 13 card bridge hand with 4 spades, 3 hearts, 2 clubs, and 4 diamonds?
7.
What is the probability of a 13 card bridge hand with 5 of one suit, 3 of a second suit, 4 of a third suit and 1 of
the last suit?