# How many cards are in a uno deck

UNO is a card game. A standard UNO deck consist of 108 cards: four each of Wild and Wild Draw Four, and 25 each of four different colors (red, yellow, green, blue). Each color consists of number cards (one zero, two each of 1 through 9) and two cards each of Skip, Draw Two, and Reverse. These last three types are known as action cards. To begin the game (using a well shuffled deck) a seven card hand is dealt to each player (without replacement). Consider an outcome space without order. Without worrying about how many players are there, find the probability of a player starting of with: a. a whole hand of action cards. b. a hand of cards with out any Wild (Wild or Wild Draw Four) cards. Explain your answer by giving a clear description of an equally-likely outcomes model on which it is based. In other words, tell me what I and events you are using, how many elements they have?

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total number of cards = N = 108
wild cards = 4
wild draw four = 4
we have 4 different colors and each color has 25 cards with
break down as
zero numbered card = 1
numbered from 1 to 9 = 2 each (total 18)
skip = 2
draw two = 2
reverse = 2
skip, draw two and reverse are action cards
therefore, in a deck of UNO we have 3*2*4 = 24 action cards
a seven card hand is dealt to each player from a well shuffled
pack of card.
therefore, as each card is equally likely, we have total
possible outcomes as 108C7
where ‘C’ function is a Combination function and it is defined
as

Ω is a event of every possible outcome and it has 108C7
= 27883218168 elements
an equally likely model is a model where equal weights are
attached to every outcome and thus the probability of each outcomes
become equal.
1) let ‘A’ be the event a whole hand is of action
cards.
we have a total of 24 action cards in a UNO deck of 108
cards.and we have to draw a hand of 7 cards
total number of outcomes for event ‘A’ is
24C7
therefore, probability that a player starting with a whole hand
of action cards is
=
= 0.0000124
therefore, a person starts with a whole hand of action
card is 0.0000124
and number of outcomes of event ‘A’ is
346104
2) let ‘B’ be the event that a hand of card is without
any wild card
therefore we have a total of 100 cards that do not have any wild
( wild or wild draw four) cards
therefore a hand of 7 out of 100 cards for event ‘B’ can be
drawn in 100C7 total ways
therefore, the probability that a player starting with a hand of
cards without any Wild (Wild or Wild draw four) cards is
=
= 0.5741
therefore, a person starts with a hand
of cards without any Wild (Wild or Wild draw four) is
0.5741
and number of outcomes of event ‘B’ is
16007560800.
n n! r!(n-r)! r
24C7 108C7
100C7 108C7

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