## If 5 items are chosen at a random without replacement from a list of 10 items, in how many ways can the 5 items be arranged if the

Question

If 5 items are chosen at a random without replacement from a list of 10 items, in how many ways can the 5 items be arranged if the order of items in arrangement is important?

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1 week 2022-12-30T20:41:35+00:00 1 Answer 0 views 0

1. Considering the definition of permutation, the items can be arranged in 30,240 ways.

### What is Permutation

Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.
That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.
In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:
• take all the elements of a set.
• the elements of the set are not repeated.
• order matters.
To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:
mPn= m!÷ (m-n)!
where “!” indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

### Ways the items can be arranged

In this case 5 items are chosen at a random without replacement from a list of 10 items.
You want to know in how many ways can the 5 items be arranged if the order of items in arrangement is important. So, you use the permutation 10P5.
10P5= 10!÷ (10-5)!
Solving:
10P5= 3,628,800÷ 5!
10P5= 3,628,800÷ 120
10P5= 30,240
Finally, the items can be arranged in 30,240 ways.