Question

how many different ways can 6 different position be filled by 12 applicants?

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

There are $665,280$ different ways to fill the 6 positions with the 12 applicants.

Explanation:

To solve this problem, we need to use the concept of permutations. A permutation is a way of arranging a set of objects in a specific order.

In this case, we want to find the number of ways to fill 6 different positions with 12 applicants. The order in which we choose the applicants matters, because different applicants may be better suited for different positions. Therefore, we need to use the permutation formula:

$nPr = n! / (n - r)!$

where n is the total number of items (applicants) and r is the number of items to be chosen (positions to be filled).

In this case, we have 12 applicants and we want to choose 6 of them to fill the 6 positions. So we have:

$n = 12$ (the total number of applicants)

$r = 6$ (the number of positions to be filled)

We can substitute these values into the permutation formula:

$nPr = n! / (n - r)!\\nPr = 12! / (12 - 6)!\\nPr = 12! / 6!$

Simplifying, we get:

$nPr = (12 \times 11 \times 10 \times 9 \times 8 \times 7) / (6 \times 5 \times 4 \times 3 \times 2 \times 1)\\nPr = 665,280$

Therefore, there are $665,280$ different ways to fill the 6 positions with the 12 applicants.

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