Homework #8 - Due December 14th by 2:00pm.

Please give it to me or slide it under my door by
that date and time.

1. How many anagrams are there of "AABBBBCCC"?  Express your answer as an integer.
   
   
2. How many ways are there to walk form A to B on the grid below, on the left, taking steps only north and east?

3. How many ways are there to walk from A to B on the grid above without passing through X?
   
   
4. How many ways are there to walk from A to B on the grid above without passing through either X or Y?
   
   
5. How many ways are there to walk from C to D on the grid above without passing through either X or Y?
   
   
6. From a class of 10 boys and 12 girls, how many 4-student committes can be formed containing:
1. 2 boys and 2 girls?
2. 3 boys and 1 girl?
3. 1 boy and 3 girls?
   
   
7. A lottery asks its players to select five distinct numbers from among the numbers 1-50.  In how many different ways can this be done?
   
   
8. How many even, five-digit numbers are there?
   
   
9. Find the value of  .
   
   
10. Find a binomial coefficient (choose number) that exactly equals .