combinations: poss. 5-card hands w/ 2 of 1 kind, 2 of 2nd, &

[myruhh]

1) Find the number of possible 5-card hands that contain: 2 of one kind, 2 of a second kind, and 1 other card. Please show me how you did it too.

2) A baseball coach is determining the batting order for the team. The team has 9 players, but the coach does not want the pitcher to be one of the first four bat. How many batting orders are possible?


I forgot the formulas, and don't even know where to start

 

[Deleted member 4993]

Re: combinations

1) Find the number of possible 5-card hands that contain: 2 of one kind, 2 of a second kind, and 1 other card. Please show me how you did it too.<<< What is a kind - same suit? Same number?

2) A baseball coach is determining the batting order for the team. The team has 9 players, but the coach does not want the pitcher to be one of the first four bat. How many batting orders are possible?

How many ways can he choose the first in line - 8 (9 - pitcher)

How many ways can he choose the second in line - 7 ( 1 already chosen - picher)

How many ways can he choose first two slots = 8 * 7 = 56

Now continue....

I forgot the formulas, and don't even know where to start

 

[soroban]

Re: combinations

Hello, myruhh!

(1) Find the number of possible 5-card hands that contain Two Pairs.

\(\displaystyle \text{There are: }\:{13\choose2} \:=\:78\text{ choices for the values of the Two Pairs.}\)

\(\displaystyle \text{There are: }{4\choose2}\cdot{4\choose2} \:=\:36\text{ ways to get the Two Pairs.}\)

\(\displaystyle \text{There are }44\text{ choices for the fifth card.}\)


\(\displaystyle \text{Therefore, there are: }\:78\cdot6\cdot6\cdot44 \:=\:\boxed{123,\!552} \text{ hands with Two Pairs.}\)