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# Tom, Jerry, and Donald and other three people sit in a line.

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Joined: 11 May 2008
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Tom, Jerry, and Donald and other three people sit in a line. [#permalink]

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04 Sep 2008, 19:52
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Tom, Jerry, and Donald and other three people sit in a line. From left to right, if Tom cannot sit on the first seat, Jerry cannot sit on the second seat, and Donald cannot sit on the fourth seat, hoe many different arrangements are possible?
(A) 720
(B) 426
(C) 432
(D) 438
(E) 444

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Joined: 15 Dec 2008
Posts: 52

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Schools: HBS(08) - Ding. HBS, Stanford, Kellogg, Tuck, Stern, all dings. Yale - Withdrew App. Emory Executive -- Accepted, Matriculated, Withdrewed (yes, I spelled it wrong on purpose). ROSS -- GO BLUE 2011.

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17 Mar 2009, 08:49
arjtryarjtry wrote:
Tom, Jerry, and Donald and other three people sit in a line. From left to right, if Tom cannot sit on the first seat, Jerry cannot sit on the second seat, and Donald cannot sit on the fourth seat, hoe many different arrangements are possible?
(A) 720
(B) 426
(C) 432
(D) 438
(E) 444

(X X X X X X) where each X is a seat.

6 permutaions of 6 = 720, which cant be right, because you have restrictions on who can sit where. Trap answer A

You have to subtract the options that have Tom in the first seat, which is 5 permutations of 5, which = 120, so your down to 600 ways. (T X X X X X)

You also can't have Jerry in the second seat, which can happen 120 ways. (X J X X X X)
That takes you to 480.
But you've already subtracted Jerry in the second seat when Tom is in the first seat, so you'll need to add those back. (T J X X X X) 4 Permutations of 4 = 24 - so where at 504

Now take away Don in the 4th seat... (X X X D X X) another 120 -- back to 384.
But, of course, you've subtraced Don on the fourth seat during (T X X D X X) so add back 24
you're at 408.
You also took Don away during the Jerry seating, so add back (X J X D X X) and you're at 432
But that means you double added (T J X D X X) so you have to remove 3 perms of 3 = 6 sp your at 426.

X X X X X X 720
- T X X X X X 120
- X J X X X X 120
+ T J X X X X 24

- X X X D X X 120
+ T X X D X X 24
+ X J X D X X 24
- T J X D X X 6

426

Kudos [?]: 120 [0], given: 1

Re: seating arrangements   [#permalink] 17 Mar 2009, 08:49
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