SOLUTION: number of ways of selecting 4 men from the row of 10 men such that no two are adjacent to each other

Question 798821: number of ways of selecting 4 men from the row of 10 men such that no two are adjacent to each other
Answer by Finavon(81) (Show Source): You can put this solution on YOUR website!
1 3 5 7 or 8 or 9 or 10
1 3 6 8 or 9 or 10
1 3 7 9 or 10
1 3 8 10
1 4 6 8 or 9 or 10
1 4 7 9 or 10
1 4 8 10
1 5 7 9 or 10
1 5 8 10
1 6 8 10
2 4 6 8 or 9 or 10
2 4 7 9 or 10
2 4 8 10
2 5 7 9 or 10
2 5 8 10
2 6 8 10
3 5 7 9 or 10
3 5 8 10
3 6 8 10
4 6 8 10
Count 35 combinations (order ignored)

If order matters :
For each combination:
A B C D
A B D C
A C B D
A C D B
A D B C
A D C B
Any one of the group of 4 can be first
with 6 permutations of the remaining 3
so 4x6 = 24 permutations of each combination.
Overall 24 x 35 = 840 permutations
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