The company has 3 delivery vans. In how many ways can the vans be parked in a row?
Answer:
6 ways
Step-by-step explanation:
We may have already heard about counting techniques and may have encountered them in probability problems, but they are absolutely difficult to understand and answer in first view.
Counting, when we talk about probability, is referring to the techniques by which we use to count and know the set of possible outcomes. And by talking about “possible outcomes“, we are referring to the dependence and independence of the events in a situation.These 2 factors are actually the main factors to determine how are we going to calculate the total possible outcomes.
For basic problems in counting like the one we have, the best way to solve the problem is to write (or if possible draw) the outcomes. That is we are to show how each element is paired with other elements. Of course this technique is only limited to small numbers of elements involved.
See problem above.
It is asking “how many ways can the 3 delivery vans be parked in a row”.
So first, we set letters to represent the vans.
1st van = A
2nd van = B
3rd van = C
Arranging the vans in order from A to C, and rearranging them placing each one on the first place, we have
ABC
BCA
CAB
Reversing the above, we have
CBA
ACB
BAC
Note that there are no other ways we can arrange them together. So counting all the number of ways we made, we have 6.
Therefore, the number of ways that the vans can be parked in a row is 6.
We can also use Permutation in this problem.
Permutation is a counting technique by which we arrange the objects without repetition, and arranging them with regards to their order.
Shortly, in permutation, we take note that each order we arrange the objects whether one arrangement has the same objects with the other is important and would count as 1.
Recall that the formula in permutation is
nPr where r=n is n!
substituting all the values, we have
3P3 = 3!
= 3 x 2 x 1
= 6
For more related problems, see links below.
https://brainly.ph/question/1085983
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https://brainly.ph/question/271680
