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in how many different ways can 5 bicycles be parked if there are 7 avaiy parking spaces??


Sagot :

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-space

B1-space-B2-B3-B4-space-B5

space-B1-B2-B3-B4-B5-space

In 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 7! / 1!1!1!1!1!2!

where

7! represents the 7 things we are arranging

the five 1!'s represent each of the distinct 5 bicycles; and

2! represents the 2 spaces that are identical.

Therefore, the number of ways that 5 bicycles can parked in parking lot with 7 spaces is 7! / 1!1!1!1!1!2! = 7!/2! = (7)(6)(5)(4)(3)(2)(1) / (2)(1) = 2530 ways.