Assume the cards are drawn sequentially and without replacement

Question

In how many ways can 5 diamonds be drawn from a standard deck of 52 cards?

Answer 1

13 chose 5 = 13!/(5!8!) = 

 

13*12*11*10*9

------------------ <---- 8! cancels out

5*4*3*2*1

 

13*12*11*9

--------------  <--- 10 cancels 5*2; 1 gets multiplied out/ignored

     4*3

 

13*11*9 <--- 12 cancels 4*3

 

1287