Question 1127575
A 3 card hand is drawn from a standard 52 card deck. 
a.) How many 3 card hands are possible?
<pre>
That's 52 cards choose 3 = 52C3 = 22100 ways to choose 3 cards.
</pre>
b.) How many hands, if all 3 cards must be of the same suit? 
<pre>
Choose the ranks: That's 13 ranks choose 3 = 13C3 = 286 ways
Choose the suit: That's 4 suits choose 1 = 4C1 = 4 ways
Answer: 286&#8729;4 = 1144 ways
</pre>
c.) How many hands, if no 2 cards are of the same suit?
<pre>
Think of the 4 suits in alphabetical order:
Clubs, Diamonds, Hearts, Spades.

Choose the 3 suits:
That's 4 suits choose 3 = 4C3 = 4 ways.

Choose the rank for the card with the suit that starts with the letter
closest to the first of the alphabet.

That's 13 ranks choose 1 = 13C1 = 13 ways

Choose the rank for the card with a suit that starts with the letter
next to the closest to the first of the alphabet.

That's 12 remaining ranks choose 1 = 12C1 = 12 ways.

Choose the rank for the card with a suit that starts with the letter
closest to the end of the alphabet.

That's 11 remaining ranks choose 1 = 11C1 = 11 ways.
 
That's 4&#8729;13&#8729;12&#8729;11 = 6864

Edwin</pre>