- #1
jaus tail
- 615
- 48
Homework Statement
Number of ways in which 6 boys and 6 girls can sit such that no 2 boys and 2 girls are together in a row.
Homework Equations
If there are n different objects in a row, then to place the we have n! ways
If n objects have n1 object of 1 kind then we have
n!/(n1)!
The Attempt at a Solution
we can have:
6 boys can sit in 6! ways
Now there are 7 spots and 6 girls so we have 7P6 (P because order matters as G1 then G2 is different from G2 then G1)
So we have 7P6 ways for girls to sit
So total number of ways is 6! times 7P6 ways which is 3628800
Book answer is 6! 6! + 6! 6! which is 1036800
Is book wrong?
Even from this link, I think book is right. But why can't we use 7P6?
GMAT Club:
https://gmatclub.com/forum/six-boys-and-six-girls-sit-in-a-row-at-random-find-the-57448.html