In how many different ways can 3 identical orange hats and 3 identical purple hats be distributed among 6 children such that each child receives a hat? Choose the most appropriate option.
A) 215  B) 20  C) 997952  D) 6169  E) 241
1st Child: 6 has options   2nd Child: 5 has options…   Therefore, for all kids: 6 x 5 x 4 x 3 x 2 = 720 arrangements.   Since the orange are identical, we divide by 3!; Since the purple are identical, we divide by another 3!   So: in all, 720/[ 3! X 3! ] = 20 ways.   (e.g. Answer: 20)
<result>B</result>
In how many different ways can 3 identical orange hats and 3 identical purple hats be distributed among 6 children such that each child receives a hat?