Question

(a) Find the probability of being dealt a "nines over kings" full house (three nines and two kings). (Round your answer to six decimal places.)

(b) Find the number of different types of full houses. (Ignoring suit.)
ways

(c) Find the probability of being dealt a full house. (Round your answer to six decimal places.)

Answer 1

(a) ways of selecting 3 of 9 cards from 4 suits = = 4

ways of selecting 2 of K cards from 4 suits = = 6

hence ways selecting above cards = 24

total ways of selecting 5 cards from deck of 52 =  

hence probability = = 0.000009

(b)

selecting 3 same cards from a deck of 52 suits (as 13 cars in each suit) = 13

selecting 2 same cards from rest cards (one card of13 cards can not be used as three of them used hence can not make the combination of 2 hence total options) = 12

hence total options = 12*13 = 156(as we have to ignore suit)

(c)

selecting 3 cars = 13 * = 13*4 = 52   

selcting 2 cars from rest = 12 * = 12 *6 = 72

ways to select 5 cars from 52 =

hence total probablity =    = 0.001440