# There are 18 people in line to use a voting ballot box. 7 of them are dressed in a red t-shirt, and the rest in a black t-shirt. In how man different ways can the queue be arranged?i) If it...

There are 18 people in line to use a voting ballot box. 7 of them are dressed in a red t-shirt, and the rest in a black t-shirt. In how man different ways can the queue be arranged?

i) If it includes a person in a red shirt in front of the line?

ii) If there are 5 people in red t-shirts in a row?

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### 1 Answer

There are 18 people in line to use a voting ballot box. 7 of them are dressed in a red t-shirt, and the rest in a black t-shirt.

In the determination of the arrangement of the persons in a line permutations have to be used as the order relevant.

If the person at the front of the line is in a red t-shirt, the number of arrangements of the line is `(17P17)/(6!*11!) = 12376`

If 5 people in red shirts are in a row, they can be considered as one unit. The number of arrangements is `(14P14)/(2!*11!) = 1092`

**If the person at the front of the line is in a red t-shirt, they can be arranged in 12376 ways and if there are 5 people in a red t-shirt in a row they can be arranged in 1092 ways.**