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Michael_Light
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Homework Statement
Suppose there is 7 chairs arranged in a straight line, each of the 3 boys will sit randomly on one of the chair . In how many ways the boys can be seated if the 3 boys cannot sit next to each other? Assume that the boys are indistinguishable.
I listed out all the possible outcomes (which is 10), but i believe there is a generalized way to find the answer. Can anyone enlighten me?
Homework Equations
The Attempt at a Solution
Let O represent seat occupied by the boys and X is empty seat.
Possible outcomes:
XOXOXOX
XOXOXXO
XOXXOXO
XXOXOXO
OXXOXOX
OXOXXOX
OXOXOXX
OXXOXXO
OXOXXXO
OXXXOXO