Answered

IDNStudy.com, ang iyong platform ng sanggunian para sa eksaktong mga sagot. Ang aming mga eksperto ay handang magbigay ng malalim na sagot at praktikal na solusyon sa lahat ng iyong mga tanong.

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

Sagot :

Noelarcallanaidn
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
[tex] \frac{7!}{1!1!1!1!1!2!} [/tex] 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 [tex] \frac{7!}{1!1!1!1!1!2!}= \frac{7!}{2!}= \frac{(7)(6)(5)(4)(3)(2)(1)}{(2)(1)}=2520 [/tex] ways.
Salamat sa iyong kontribusyon. Huwag kalimutang bumalik upang magtanong at matuto ng mga bagong bagay. Ang iyong kaalaman ay mahalaga sa ating komunidad. Para sa mabilis at maasahang mga sagot, bisitahin ang IDNStudy.com. Nandito kami upang tumulong sa iyo.