Probability with Combinations?

Question

Please help me! I'm so confused! Please include all steps AND helpful tips that will help me solve these kinds of problems (problems with probability and combinations)! Thanks a lot!

 

A 5 card hand is dealt from a deck of 52 cards what is the probability that none of them are queens?

 

A 7 card hand is dealt from a deck of 52. What is the probability that the hand includes all four kings?

 

Eleven dimes where tossed. Find the probability that the 7th one only was heads.

Answer 1

A 5 card hand is dealt from a deck of 52 cards what is the probability that none of them are queens?

There are ₅₂C₅ ways to deal a five card hand form the deck.  There are ₄₈C₅ ways of dealing a five card hand from a deck, none of which cards are queens. The probability is

₄₈C₅/₅₂C₅=48×47×46×45×44/(52×51×50×49×48)=0.658841998

 

A 7 card hand is dealt from a deck of 52. What is the probability that the hand includes all four kings?

₄₈C₃×₄C₄/₅₂C₇=0.000129282

 

Eleven dimes were tossed. Find the probability that the 7th one only was heads.

The requirement is for the sequence to be 6 tails, 1 head, 4 tails.  This is the only way to do it.

 

The probability of any single sequence of 11 tosses of a fair coin is 1/2¹¹=1/2048