A man has 6 friends. In how many ways he can invite one or more of his friends at a dinner?
Step-by-step Solution:
The number of ways a person can invite friends is based on selecting subsets of his 6 friends. The total number of subsets of a set with (n) elements is given by: \[\] \( 2^n \) \[\] where (n) is the number of elements in the set.\[\] Here, the number of friends is 6, so the total number of subsets of his 6 friends is: 2^6 = 64 \[\] However, this total includes the empty set, which represents inviting no friends. The question specifies that we need to invite one or more friends, so we subtract the empty set:\[\] 64 - 1 = 63 \[\] \[\] \[\] Correct Answer: (c)