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Suppose we want to choose 5 letters, without replacement, from 9 distinct letters. If the order of the choices is relevant, how many ways can this be done?2 points

Question

Suppose we want to choose 5 letters, without replacement, from 9 distinct letters. If the order of the choices is relevant, how many ways can this be done?2 points

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Solution

The problem can be solved using the concept of permutations.

In permutations, the order of selection is important. The formula for permutations is:

P(n, r) = n! / (n-r)!

where:

  • n is the total number of items,
  • r is the number of items to choose,
  • "!" denotes factorial, which is the product of all positive integers up to that number.

In this case, we have 9 distinct letters (n=9) and we want to choose 5 of them (r=5), so we plug these values into the formula:

P(9, 5) = 9! / (9-5)!

= 9! / 4!

= (987654321) / (432*1)

= (98765)

= 15,120

So, there are 15,120 ways to choose 5 letters from 9 distinct letters when the order of the choices is relevant.

This problem has been solved

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