A person has 8 friends. The number of ways in which he may invite one or more of them toa dinner is.(a) 250 (b) 255 (c) 200 (d) none of these
Question
A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is:
- (a) 250
- (b) 255
- (c) 200
- (d) none of these
Solution
To find the number of ways in which the person can invite one or more of his 8 friends to dinner, we can use the concept of combinations.
For each friend, there are two possibilities: either they are invited or they are not invited. Since there are 8 friends in total, we have 2 options for each friend.
Using the multiplication principle, we can multiply these options together to find the total number of ways to invite the friends.
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^8 = 256
However, we need to subtract 1 from this total because we are not considering the case where no friends are invited.
Therefore, the correct answer is (b) 255.
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