# Combinations

• May 19th 2009, 05:58 PM
Nisar_0926
Combinations
hey guys can anyone help me with question b) c) and d) i am really confused for some reason i am not getting the correct answer.

18) Twenty-Four girls try out for the senior softball team at St. Marcellinus. In how many ways can a team of 9 fielders (1 pitcher, 1 Catcher, 4 Infielders, 3 Outfieders) be selected given each of the following conditions?

a) any girl can play any position.

so for a) it is 24C9 = 1 307 504

b) Of the girls trying out are Pitchers, 5 are Catchers and the other trying out play any of the other 7 field positions.

c) Emily must be pitcher and Jeannie must be the catcher, but the other girls can play any other position.

d) Louise cannot be on the team

b) 194 480
c) 170 544
d) 817 190

• May 19th 2009, 11:23 PM
noob mathematician
Quote:

Originally Posted by Nisar_0926

b) Of the girls trying out are Pitchers, 5 are Catchers and the other trying out play any of the other 7 field positions.

b) Is the number of pitchers given?

c) ${22 \choose 7}$

d) ${23 \choose 9}$
• May 20th 2009, 02:34 AM
Villa Incognito
Quote:

Originally Posted by noob mathematician
b) Is the number of pitchers given?

c) ${22 \choose 7}$

d) ${23 \choose 9}$

I agree with your answers, I liked this topic in highschool (Giggle).

I think its important to understand why though, instead of just giving the answers.

c) 2 of the positions have been chosen, which means out of the 24 girls there are only 22 who can fill the remaining positions (and since 2 are taken, that leaves only 7 to be filled)

d) same sort of thing, try to figure out why yourself
• May 20th 2009, 07:23 AM
Nisar_0926
nope for b) the number of pitchers are not given thats how the question is worded.

But is it repressenting the 1 pitcher as written in the question?
• May 20th 2009, 09:55 PM
noob mathematician
Quote:

Originally Posted by Nisar_0926
nope for b) the number of pitchers are not given thats how the question is worded.

But is it repressenting the 1 pitcher as written in the question?

Oh that's the question?
Hm.. well I suppose there are two pitchers but is missed out in the question.

So Assuming there are two pitchers to choose from, it will be

${2 \choose 1}{5 \choose 1}{17 \choose 7}= 194480$