singhsa wrote: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
OA - C
For the moment, let's ignore the stipulation that the 4th and 6th models cannot be placed adjacent to each other.
If we choose any 5 models, there will be only 1 way to arrange them: from shortest to tallest. So any combination of 5 gives us 1 possible arrangement.
Number of possible combinations = 7C5 = 21. So there are 21 ways to arrange the models from shortest to tallest.
Since a few of these arrangements will be bad -- those that place the 4th and 6th models next to each other -- we need an answer choice just a bit less than 21.
The correct answer is C.
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