# Combinations-Number of choices

1. Joey is having a party. He has 10 friends, but his mom told him he could only invite 6 of them. How many choices are there if

a. there are no restrictions

b. there are 2 brothers who will only attend if they can attend together

c. there are 2 girls who each will not attend if the other one does

https://brainmass.com/math/combinatorics/combinations-number-choices-32738

#### Solution Preview

a) there are no restrictions

Total no friends= 10

If there are no restrictions then the no of choices = no of ways of choosing 6 out of 10 =

10 C 6 = (10 x 9 x 8 x 7 x 6 x 5 ) / ( 1 x 2 x 3 x 4 x 5 x 6 ) = 210

Answer : 210

b ) there are 2 brothers who will only attend if they can attend together

There are 2 cases here:

Case 1 ) Both brothers attend

In this case there are 4 more friends to ...

#### Solution Summary

The expert calculates the number of choices.

$2.19