Question

3 identical cans of cola, 2 identical cans of iced tea and 3 identical cans of orange juice are arranged in a row. Calculate the number of arrangements if the 3 cans of cola are all next to each other and the 2 cans of iced tea are NOT next to each other.
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Answer 1

Answer:

There are 18 ways of arrangement.

Step-by-step explanation:

• Choose a group of three spots for the sodas. They number five.

• Choose 2 separate locations for the green tea now.

• The slots utilised for the drink determine how many of them are offered.

• There are three ways to arrange the tea if the sodas are at each end of the display.

• There are four different methods to put up the tea if they are in any other group of three slots.

• You simply need to write this down and persuade yourself of it.

• After placing the tea and sodas, the juice simply fills the last three spaces.

• Therefore, there are a total of 2 * 3 + 3 * 4 = 18 arrangements.

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Answer 2

Answer:

The number of arrangements is 18.

Step-by-step explanation:

• Choose a set of 3 slots for the sodas. The number five.
• Now select 2 non-adjacent slots for the green tea.
• How many of these exist available depends on the slots utilized for the soda.
• If the sodas exist at either end of the display, then there exist 3 methods to arrange the tea.
• If they exist in any other set of 3 slots then there exist 4 ways to arrange the tea.
• You will just have to put a pencil on paper and persuade yourself of this.
• Having set the sodas and the tea the juice just takes up the staying two slots.

Therefore, there exist $2 * 3 + 3 * 4 = 18$ total arrangements.

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