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Probability with Combinations?

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.
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1 Answer

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
 
 
 
 

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