In how many different ways can 5 bicycles be parked if there are 7 available parking spaces

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Seven friends on bicycles find an empty bike rack with exactly 7 spots for bikes. How many ways can the 7 bikes be parked so Chantalle, Amy and Maria are parked next to each other?

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_ 17. In how many ways can bicycles be parked if there are available parking spaces?

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This is an example of a problem that involves Permutation with Repetition.Notice that we have 7 available parking spaces for only 5 bicycles. This means that if we call our 5 bicycles B1, B2, B3, B4, and B5, the following are just few examples that are distinct from each other:B1-B2-B3-B4-B5-space-spaceB1-space-B2-B3-B4-space-B5space-B1-B2-B3-B4-B5-spaceIn other words, aside from the 5 bicycles we are arranging, we are also taking into account the arrangement of the 2 extra spaces.So really, we are arranging 7 things here with two objects (the spaces) being alike. This can be solved by translating it as

Therefore, the number of ways that 5 bicycles can parked in parking lot with 7 spaces is