varun289 wrote:269. 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
Let the 7 models be the integers 1-7, with 1 the shortest and 7 the tallest.
Good arrangements = (total arrangements) - (arrangements in which 4 and 6 are adjacent).
Total arrangements:
For any combination of 5 models chosen, there will be only one acceptable arrangement: from shortest to tallest.
Thus, the total number of arrangements is equal to the total number of COMBINATIONS OF 5 that can be formed from the 7 models:
7C5 = (7*6*5*4*3)/(5*4*3*2*1) = 21.
Arrangements in which 4 and 6 are adjacent:
Since the arrangement must include 46, and the integers must be in ascending order, 5 cannot be used here.
Thus, from models 1, 2, 3 and 7, we need to choose a COMBINATION OF 3 models to be put together with 46.
Number of combinations of 3 that can be formed from 4 choices = 4C3 = (4*3*2)/(3*2*1) = 4.
Good arrangements = 21-4 = 17.
The correct answer is
C.
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