SOLUTION: two cards drawn in succession from a deck without replacement .what is the probability that both cards are greater than 3 and less than 9?

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Question 812373: two cards drawn in succession from a deck without replacement .what is the probability that both cards are greater than 3 and less than 9?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
There are five "successful" ranks of cards 4,5,6,7,8 and each 
has 4 suits, So there are 5×4 or 20 "successful" cards in a deck.

The probability that the first card drawn is a "successful" card is 20 out of
52 or  or .

When a successful card is drawn, that leaves a deck of 51 cards that contains
19 successful cards.   

So ths of the times when a successful card is drawn the first time,
we will then draw a successful card the second time ths of the time.

Therefore sts of those ths of the time, we will draw
two successful cards in a row.

Answer × =   

If can be calculated .

On a TI-83 or 84,  (20 nPr 2)/(52 nPr 2) or (20 nCr 2)/(52 nCr 2).

Edwin
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