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Arrange 6 people in a row such that the bride must be left of the groom.

A) 720
B) 360
C) 120
D) 24

1 Answer

5 votes

Final answer:

To arrange 6 people with the bride left of the groom, first, treat the bride and groom as one unit. There are 5! ways to arrange 5 units, which is 120. Since we only consider valid arrangements for the bride and groom, the answer is C) 120.

Step-by-step explanation:

The problem asks us to arrange 6 people in a row with the condition that the bride must be to the left of the groom. This is a problem related to permutations and combinations, a fundamental concept in mathematics that deals with the arrangement of items within a specific set of rules.

To solve this, first, consider the bride and groom as a single unit since the bride must always be to the left of the groom. This temporarily reduces our problem to arranging 5 units (4 people + 1 couple). These 5 units can be arranged in 5! (factorial) ways, which means 5 x 4 x 3 x 2 x 1 = 120 ways. However, within this unit of the bride and groom, there are 2 arrangements: the bride can be to the left or to the right of the groom. As per our condition, we only consider the one where the bride is to the left of the groom.

Therefore, for each of the 120 arrangements of the 5 units, there is only 1 valid arrangement of the bride and groom. This means the total number of arrangements where the bride is left of the groom is 120. The correct answer does not change, regardless of considering one arrangement or two for the bride and groom within their unit because we are only counting the valid one as per the question's condition.

Thus, the final answer is 120, which corresponds to option C.

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