Probability word problem

Question

Antonella has 5 different T-shirts that she can hand out to 3 different people. If each person gets only 1 T-shirt, how many different combinations of T-shirts are possible?

Answer 1

Here's the hard way:

Starting with A:

A

   AB

      ABC

      ABD

      ABE

   AC

      ACD

      ACE

   AD

      ADE

B

   BC

      BCD

      BCE

   BD

      BDE

C

   CD

      CDE

 

There are 10 possible combinations.

 

Charles's method is the easy way.  Here's how it works:

There are 5*4*3 = 60 permutations for 3 out of 5 shirts.    [That's 5! / 2!.]

This includes all combinations in all possible orders.

That means that each group of 3 will be included 3*2*1 = 6 times.  [That's 3!]

60 / 6 = 10      [That's (5! / 2!) / 3!, or 5! / (2! * 3!)].

 

I hate to memorize formulas.  I can remember it this way!

Answer 2

So 5 different t-shirts to give to 3 people and each person gets only one t-shirt. Think a b c d e t-shirts.

This is a combination problem.

5! / (3! * 2!) = 5*4 / 2 = 10.

There are 10 ways.