probability

Question

What is the probability that a five-card poker hand contains cards of five different kinds and does not contain a flush or a straight?

Comments

no of ways according to the question can be calculated as :

Total no of ways of selecting 5 cards from 52 cards

- Total no of straight - Total no of flush - Total no of flush AND straight

C(52, 5) - 10 * 4 ^ 5 - C(13, 5) * 4 - 10

correct me if i am wrong???

Answer 1

Kinds=13

Suits=4

Consecutive kinds=10

 

Five diff. kinds=diff kinds(13C5) * each kinds have four suit( 4^5)=1317888 = Diff kinds + (Flush union Straight)

Flush= Kinds can be anything but all of them should be from same suit=Kinds(13C5) * Suits(4C1)=5148

Straight=consecutive kinds (10C1) * suit can be anything(4^5)=10240

Flush intersection Straight = Same Suit (4C1) * consecutive kinds(10C1)=40

Flush union Straight=5148+10240-40=15348

Diff kinds with neither Flush nor Straight=1317888-15348=1302540

So probability= 1302540/52C5