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Combinations-Number of choices

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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

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The expert calculates the number of choices.

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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 ...

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