A person has 5 tickets for a concert and she wants to invite 4 of her 8 best friends. How many choices does she have, if two of her friends do not get along and cannot be both invited?

55

Step-by-step explanation:

Combinations formula is used to make choice of 'R' out of 'N' options =

N (C) R = N! / [ R!. (N-R) ! ]

Total choices to choose 4 out of 8 friends = 8C4

= 8! / (4! 4!)

= 70

Choices for calling them 2 together = 2C2 x 6C2

= 1 x [ 6! / (2! 4!) ]

= 15

So : Number of choices that the 2 friends are not called together = Total choices - choices they are called together

= 70 - 15 = 55