Out of seven models, all of different heights, five models will be chosen to pose for a photograph. If the five models are to stand in a line from shortest to tallest, and the fourth-tallest and sixth-tallest models cannot be adjacent, how many different arrangements of five models are possible?	Choose the correct choice from the following
A) 6	B) 11	C) 17	D) 72	E) 210
Total no. of ways "5 models can be selected from 7" = 7C5 = 21.   Fourth tallest and Sixth tallest can never stand adjacent to each other. Also, all selected models will be lined up from shortest to tallest.   Hence, we have to pull out the no. of ways 4 &amp; 6 stand adjacent to each other from the above total, i.e = 21.   The following will be the way in which 4 &amp; 6 stand close to each other.   1 2 3 4 6   1 2 4 6 7   1 3 4 6 7   2 3 4 6 7   So, the answer will be   21-4= 
<gadget id="calculator">  21-4</gadget>
<output>17</output>
17 ways.   ANS:17
<result>C</result>
Out of seven models, all of different heights, five models will be chosen to pose for a photograph. If the five models are to stand in a line from shortest to tallest, and the fourth-tallest and sixth-tallest models cannot be adjacent, how many different arrangements of five models are possible?