SOLUTION: In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats? (A) 6 (B) 9 (C) 12 (D) 36 (E) 720

Question 3654: In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?
(A) 6
(B) 9
(C) 12
(D) 36
(E) 720
Answer by Zenock(15) (Show Source): You can put this solution on YOUR website!
We can user mathmatical equations to solve this or we can simply think about it...
First of all we know that the boys are going to be in the 1st,3rd, and 5th seats. So the girls must be in the 2nd, 4th, and 6th seats.
So the first question we should ask ourselves is how many ways can 3 boys be arranged in 3 seats.
Lets say our boys are named A, B, and C inspiring names I know...
We can have ABC, ACB, BAC, BCA, CAB, or CBA 6 ways to arrange the boys.
Now for each way there is to arrange a the boys, there are six ways to arrange the girls (same arguement for finding the number of ways to arrange the boys).
Therefore: there are 6*6 ways to arrange the boys and girls.
The answer is (D) 36
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