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dghosh2602
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Mon Feb 16, 2009 2:36 am
G, M, P, J, B and C are supposed to sit in 6 different seats. But M and J won't sit together, how many different arrangements are possible?
So, I know I can calculate the possibilities w/o constraints and subtract the possibilities with constraints and get the answer as 6! - 5! to get 480. What I am trying to think is in terms of the following (which works for most problems, but I can't figure out why this model doesn't fit this situation)
I have 6 possibilities for Seat 1 and I assume its M, so possibilities = 6.
Now, I have 4 possibilities for Seat 2 because J won't sit with M, so possibilities = 4
Now, I have 4 possibilities again for Seat 3 because M is back in the group, so possibilities = 4
And then finally 3 and 2, so possibilities = 3 * 2
Multiplying, 6 * 4 * 4 * 6 = 576 possibilities.
Where am I formulating this wrongly?
Thanks in advance
So, I know I can calculate the possibilities w/o constraints and subtract the possibilities with constraints and get the answer as 6! - 5! to get 480. What I am trying to think is in terms of the following (which works for most problems, but I can't figure out why this model doesn't fit this situation)
I have 6 possibilities for Seat 1 and I assume its M, so possibilities = 6.
Now, I have 4 possibilities for Seat 2 because J won't sit with M, so possibilities = 4
Now, I have 4 possibilities again for Seat 3 because M is back in the group, so possibilities = 4
And then finally 3 and 2, so possibilities = 3 * 2
Multiplying, 6 * 4 * 4 * 6 = 576 possibilities.
Where am I formulating this wrongly?
Thanks in advance
