Question

A pinochle deck consists of two copies each of the 9, 10, J, Q, K and A cards of all 4 suits, for a total of 48 cards. You draw 5 cards at random from a pinochle deck

a. what is the probability of drawing a flush ( all 5 cards are the same suit)?

b. What is the probability of drawing a full house ( 3 cards of one value, 2 cards of a different value)?

Use nCn

Answer 1

total cards in each suit =12

total suit = 4

a)

5 cards of same suit can be draw in 12C5 ways and each suit can be draw in 4C1 ways

and total 5 cards can be draw from 48 cards in 48C5 ways

so, P(drawing flush) = 12C5*4C1/48C5

=0.00185

b)

there are total 8 cards of each value

and total values are 6

Pick a type of card: 6C1 ways
Pick 3 of that type of card: 8C3 ways
Pick a different type of card: 5C1 ways
Pick 2 of that type: 8C2 ways

no of 5 card hands: 48C5 ways
P("full-house hands") =(6C1*8C3*5C1*8C2)/48C5

=47040/1712304=0.0275

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