The Fundamental Counting Principle

[waloshin]

Know I know this is like grade 1 math , but I am just checking to see if I got these right.

Permutations and Combinations

1) From a standard deck of cards, how many 10 card hands are possible if you must have 3 hearts, 4 diamonds, 2 spades and 1 club?

13c3 * 13c4 * 13c2 * 13c1 = 286*715*78*13 = 207352860

2) From a standard deck of cards,how many different 10 card hands are there that contain exactly 4 hearts and 3 diamonds?

13c4 * 13c3 * 52c3 = 715*286*22100 = 41519229000

3) In how many ways can a graduating class of 30 students pick a president, secretary and treasurer in that order?

30p3 = 24360

4) How many arrangements of 4 letters can be made by using different letters from the word HOLIDAY?

7*6*5*4 = 840

5) A coach has decided on the 9 players he wants to start the final. In how many ways can he make his batting lineup?

9! = 362880

Thanks!

 

[waloshin]

C = Combination

P = Permutation

! = Factorial

5*4*3*2*1 = 120

5! = 120

 

[MegaMillions]

I'm not sure how to read the card problems, but the rest of them seem correct to me.

edit: Actually, the graduating class one has a problem. 30p3 is 30,000. 30 x 29 x 28 is 24,360. I'm not sure which is the correct answer to the problem but I know that 30p3 is not 24,360.