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probability :(

by mehaksal » Sun Aug 26, 2012 12:34 am
A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
A. 5
B. 6
C. 9
D. 24
E. 36
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by adthedaddy » Sun Aug 26, 2012 3:27 am
Hi, remember two conditions as given before arranging
1) The heights of the people within each row must increase from left to right
2) Each person in the second row must be taller than the person standing in front of him or her

Let the persons be 1,2,3,4,5,6 in increasing order of their heights.

From above conditions, We need to fix the positions of person 1 and person 6.

1 will be at the extreme left of the first row and 6 will be at the extreme right of the 2nd row.

_ _ 6
1 _ _

Now we can arrange 2,3,4,5 such that they are increasing from left to right and the person standing in 2nd row is taller than the one in the first.

This can be simply done in 4C2 ways = 6 ways. But one of the arrangement includes 4,5 together in the first row which is not possible, hence 6-1 = 5 ways is the answer.

Showing all the 5 possible ways as follows -

4 5 6
1 2 3

3 5 6
1 2 4

3 4 6
1 2 5

2 5 6
1 3 4

2 4 6
1 3 5

Hence, ans is Option (A)
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