In how many ways can a group of 5 boys and 5 girls be seated in a row of 10 seats?
Still having some confusion with the difference between combinations and permutations. I have tried this problem using both combination and permutation with the formulas and my calculator and neither were correct answers.
Best Answer
Ladies first: choose $5$ fixed places for the girls: $\binom{10}{5}$ - this (number of combinations) does not account for the order of the girls, whom you can permute in $5!$ ways. There are $5$ remaining places for the boys: Again, we can permute them in $5!$ ways. So the number is $$\binom{10}{5}\cdot 5!\cdot 5!=\ldots$$ You shouldn't find it surprising that the answer is $10!$ - that's because you are in fact permuting $10$ people over $10$ seats, no matter who is boy or girl.