SOLUTION: if five cards are drawn at random from a deck of 52 cards, what is the probability that first card is spades, second is diamonds, third is hearts, fourth is spades and fifth is clu

Here is a deck of cards:


 
A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ 
A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦
A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  
A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣  Q♣  K♣ 

There are:

13 hearts
13 diamonds
13 spades
13 clubs
-----------
52 cards total

Now 13 times out of 52 we will draw a spade first.  That's a probability
of 13/52, which reduces to 1/4.  

Now when we have drawn a spade first, there are only 51 cards left in the deck.

13 hearts
13 diamonds
12 spades
13 clubs
-----------
51 cards total

Now 13 times out of 51 we will draw a diamond second.  That's a probability
of 13/51, which doesn't reduce.  So the probability of drawing a spade,
and then a diamond is 

Now when we have drawn a spade first, and a diamond second, there are only 
50 cards left in the deck.

13 hearts
12 diamonds
12 spades
13 clubs
-----------
50 cards total

Now 13 times out of 50 we will draw a heart third.  That's a probability
of 13/50, which doesn't reduce.  So the probability of drawing a spade,
then a diamond, and then a heart is  

Now when we have drawn a spade first, and a diamond second, and a heart
third, there are only 49 cards left in the deck.

12 hearts
12 diamonds
12 spades
13 clubs
-----------
49 cards total

Now 12 times out of 49 we will draw a spade fourth.  That's a probability
of 12/49, which doesn't reduce.  So the probability of drawing a spade,
then a diamond, then a heart, and then a spade is  

Now when we have drawn a spade first, and a diamond second, a heart
third, and a spade fourth, there are only 48 cards left in the deck.

12 hearts
12 diamonds
11 spades
13 clubs
-----------
48 cards total

Now 13 times out of 48 we will draw a club fifth.  That's a probability
of 13/48, which doesn't reduce.  So the probability of drawing a spade,
then a diamond, then a heart, then a spade, and finally, a club is 

 

Multiplying all the numerators and then all the denominators,
That works out to be  which upon dividing
top and bottom by 12 reduces to , and the decimal
approximation is 



Round it however you were told.

Edwin