probability problem with condition

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r_walid: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Wed Jan 21, 2009 2:24 pm; Thanked: 1 times

by r_walid » Sun Nov 15, 2009 12:32 pm

out of 7 models, 5 will be selected for a photo. if the 5 models are to stand in a line from shortest to tallest and if all are of different heights, and if the fourth and sixth tallest models cannot sit side by side, how many different arrangements of 5 models are possible?

6
11
17
72
210

Please explain with DETAIL your reasoning.

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Source: Beat The GMAT — Problem Solving | Sun Nov 15, 2009 12:32 pm

palvarez: Master | Next Rank: 500 Posts; Posts: 199; Joined: Sat Oct 24, 2009 4:43 pm; Thanked: 22 times; GMAT Score:710

by palvarez » Mon Nov 16, 2009 11:21 am

7c5 = 21 ways without any restrictions.

4 and 6 can't sit side by side, meaning that whenever 4 and 6 are present, we need 5.

Find ways where 4 and 6 are present, but not 5: 4c3 ways = 4

21 - 4 = 17.

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gmat620: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Thu Mar 12, 2009 2:39 am; GMAT Score:620

by gmat620 » Wed Nov 18, 2009 9:32 pm

good explanation by palvarez !!

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Birgit Anne: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Thu Nov 26, 2009 6:51 am

by Birgit Anne » Mon Nov 30, 2009 11:41 am

I do not understand your last step:

If Model #6 and Model #4 are selected, but Model #5 is not, why is this 4C3?

Is it because there are 4 models left and three of them have to be choosen in order to have a total of 5 models selected?

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palvarez: Master | Next Rank: 500 Posts; Posts: 199; Joined: Sat Oct 24, 2009 4:43 pm; Thanked: 22 times; GMAT Score:710

by palvarez » Mon Nov 30, 2009 11:49 am

Birgit Anne wrote:I do not understand your last step:

If Model #6 and Model #4 are selected, but Model #5 is not, why is this 4C3?

Is it because there are 4 models left and three of them have to be choosen in order to have a total of 5 models selected?

Yes, 4 left off of 7: 4 and 6 are pre-selected, we dont wanna select 5. so, we are left with remaining 4.

Since we preselected 2, we need to pick remaning 3 from above 4.

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