1. 2*(26³*10³) [5.1.18]

2. You can choose 21*21 integer pairs. In the given range 11 are even, 10 are odd. So: (11*11 + 10*10)/21*21 [5.1.20]

3. Count the numbers from 00000 to 99999 - how many 5's appear? C(n,1)*9⁴+C(n,2)*9³+C(n,3)*9²+ C(n,4)*9¹ + 1. [5.1.30]

4.(n+1)⁴ - 1 -- you can pick 0 .. n of any letter, but you can't pick all 0s (hence the - 1 term)

5. 7! / 2!

6. C(26,6)

7. (13!)⁴ / ((52!)/(4!)¹³)

8. 20*19*18...*11

9. 4! * (5*6*7)

10.

-- RobbieMoll - 2012-04-26