ABCDEF
Let S be the set of all possible sequences A = { } such that . (In S doesn't exist A and B such that A{a} = B{a} and A{b} = B{b} and... and A{f} = B{f}.)
Find
The answer is 711521944864290.
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1 solution
We have 110 people (in the line) and we must divide them into 6 groups and in every select their captain. It is easy to see that number of possible combinations of groups and captains is that wanted sum. Considering that, we need to add 5 people more to get 6 separate groups; and we need to choose 6 captains; so, we need to choose 11 people in the line and going from left to right or right to left, there will be: first captain, first divider, second captain, second divider, ... , sixth captain. That number is ( 1 1 1 1 5 ) or 711521944864290.