# Combinations #1

• Dec 9th 2009, 10:57 AM
BabyMilo
Combinations #1
A class contains 10 boys and 15 girls. 8 can go to a local castle, 7 can go to the theatre and the remainning 10 will go to the museum.

In how many ways can the class be divided for their activity day if the group going to the theatre must consist of 4 girls and 3 boys.

thanks!
• Dec 9th 2009, 12:03 PM
Soroban
Hello, BabyMilo!

Quote:

A class contains 10 boys and 15 girls.
8 can go to a local castle, 7 can go to the theatre, the remainning 10 will go to the museum.

In how many ways can the class be divided for their activity
day if the group going to the theatre must consist of 4 girls and 3 boys?

Choose 4 girls to go to the theatre: . ${15\choose4} = 1365$ ways.

Choose 3 boys to go to the theatre: . ${10\choose3} = 120$ ways.

The other 18 students are divided into a group of 8 and a group of 10.
(Their genders do not matter.) .There are: . ${18\choose8,10} = 43,\!758$ ways.

Therefore, there are: . $1365 \times 120 \times 43,\!758 \;=\;7,\!167,\!560,\!400$ ways.

• Dec 9th 2009, 01:00 PM
BabyMilo
Quote:

Originally Posted by Soroban
Hello, BabyMilo!

Choose 4 girls to go to the theatre: . ${15\choose4} = 1365$ ways.

Choose 3 boys to go to the theatre: . ${10\choose3} = 120$ ways.

The other 18 students are divided into a group of 8 and a group of 10.
(Their genders do not matter.) .There are: . ${18\choose8,10} = 43,\!758$ ways.

Therefore, there are: . $1365 \times 120 \times 43,\!758 \;=\;7,\!167,\!560,\!400$ ways.

thanks for you reply but the answer in the back is 4 181 076 900
but again this could be wrong.