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A photographer will arrange 6 people of 6 different heights [#permalink]

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17 Oct 2008, 09:54

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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?

If we denote the persons in the increasing order of height with numbers then, these would be 1,2,3,4,5,6

Now, in the first row, first place can be occupied only by one person - 1. Second place can be occupied by 2,3,4 - total 3. Third place can be occupied by 3,4,5 - total 3.

If we denote the persons in the increasing order of height with numbers then, these would be 1,2,3,4,5,6

Now, in the first row, first place can be occupied only by one person - 1. Second place can be occupied by 2,3,4 - total 3. Third place can be occupied by 3,4,5 - total 3.

Hence, total of 1*3*3 = 9 possibilities.

can you explain the parts I have marked red above.

If we denote the persons in the increasing order of height with numbers then, these would be 1,2,3,4,5,6

Now, in the first row, first place can be occupied only by one person - 1. Second place can be occupied by 2,3,4 - total 3. Third place can be occupied by 3,4,5 - total 3.

Hence, total of 1*3*3 = 9 possibilities.

can you explain the parts I have marked red above.

IMHO, Second place can NOT be occupied by "4"

You are right. I made a mistake in a hurry. There are only 5 possible arrangements.

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?