Question

There are two lines of students. The first line has students s1, s2, s3, s4 and s5, in that order. The second line has students t1, t2, t3, t4, t5, and t6, in order. Both lines will be merged into one as follows: If both lines still have students in them, one of the two lines is randomly selected and the person in the front of that line will go to the back of the merged line. If only one line remains, then all of those students will join in the back of the merged line, in their original order. For example, one way in which the students could line up is: s1, t1, t2, t3, s2, t4, t5, s3, t6, s4 and s5. Using this procedure, how many possible ways could these 11 students line up?

Answer 1

Answer is .

{11}

SOLUTION Given the conditions , we have to find out the number of possible ways these 11 students line up. A 11-student line can be thought of as 11 places to be filled. 1 2 3 4 5 6 7 8 9 10 11 From the 11 spots above, if we randomly pick 5 spots to be filled by students 51,52, 53, 54 and 85, then they can fill those 5 spots in only one way - in the ascending order from left to right. Similarly, the students t1, tz, t3, 44, t5 and to can fill the remaining spots in only one way from left to right (ascending order). So, now we only have to find out the number of ways of choosing 5 spots from the given 11 spots randomly. This total number of ways is hCG Ans.