Question

In how many ways can 10 boys and 5 girls sit around a circlar table

Answer 1

Generate all possible combinations of 15 digits where all the digits are either one or zero. 1= boys, and 0= girls. Store all the combinations in a. Then find only the combinations of 15 digits whose digit sum is 10 - which is all the combinations with 10 boys and 5 girls. Select all those combinations and store them in b, and count them.

#b=.a#~10=+/"1 a=.odo 15#2

3003

So there are 3003 possible fifteen-digit combinations of 10 boys and 5 girls.