discussion6Ch3_2Exe20

Discussion 6

Chapter 3.2 Exercise 20

20. A six-card hand is dealt from an ordinary deck of cards. Find the probability that:

a) All six cards are hearts.

\[\binom{13}{6} / \binom{52}{6}\] = 1716 / 20358520 = 0.000084

b) There are three aces, two kings, and one queen

\[\binom{4}{3}\binom{4}{2}\binom{4}{1} / \binom{52}{6}\] = 4x6x4 / 20358520 = 0.000047

c) There are three cards of one suit and three of another suit.

\[\binom{4}{2} . \left (\binom{13}{3}\binom{13}{3}/ \binom{52}{6} \right )\] = 6 x ( 286 x 286 / 20358520 ) = 0.0241