Suppose we label the seats seat 1, seat 2, seat 3, seat 4, and seat 5.
We can choose the child for seat 1 any of 10 ways.
For each of those 10 ways we can choose the child for the
seat 1, there are 9 children left to choose to sit in
seat 2.
That's 10*9 or 90 ways to choose children to sit in seats
1 and 2.
For each of those 10*9 or 90 ways we can choose the children
for seats 1 and 2, there are 8 children left to choose to
sit in seat 2.
That's 10*9*8 or 720 ways to choose children to sit in seats
1, 2 and 3.
For each of those 10*9*8 or 720 ways we can choose the children
for seats 1, 2 and 3, there are 7 children left to choose to
sit in seat 4.
That's 10*9*8*7 or 5040 ways to choose children to sit in seats
1, 2, 3 and 4.
For each of those 10*9*8*7 or 5040 ways we can choose the children
for seats 1, 2, 3, and 4 there are 6 children left to choose to
sit in seat 5.
That's 10*9*8*7*6 or 30240 ways to choose children to sit in
seats 1, 2, 3, 4 and 5.
That's the permutations of 10 things taken 5 at a time or
"10 position 5" or P(10,5) = 10*9*8*7*6 = 30240.
Edwin
