Question

A school announced the opening of posts for 6 teachers in the local newspaper. 12 persons applied for the jobs. Can you tell in how many different ways this selection can be made ?

Answer 1

Given: A school announced the opening of posts for 6 teachers in the local newspaper. 12 persons applied for the jobs.

To find: In how many different ways this selection can be made.

Solution:

A particular event can take place in several ways and the number of ways in which an event can occur can be calculated using permutations. The following formula can be used to find the permutations of an event.

$^{n} P _{r} = \frac{n!}{(n-r)!}$

Here, n is the total number of possibilities, r is the number of positions that can be taken up by the possibilities and the symbol "!" indicates factorial. In the given question, n is 12 and R is 6.

$^{12} P _{6} = \frac{12!}{(12-6)!}$

       $= \frac{12!}{6!}$

       $= 6,65,280$

Therefore, this selection can be made in 665280 ways.

Answer 2

Given: A school announced the opening of posts for 6 teachers in the local newspaper. 12 persons applied for the jobs.

Find: How many different ways this selection can be made?

Solution:

$nP_{r}$=$\frac{n!}{(n-r)!}$

n= Number of persons that are applied for the job.

r= Number of posts that can be taken up from the persons who are applied.

So, n=12 and r=6

$12P_{6}=\frac{12!}{(12-6)!}$

       = $\frac{12!}{6!}$

       =$\frac{12X11X10X9X8X7X6!}{6!}$

       = 12×11×10×9×8×7

       = 6,65,280.

Final answer: There are 6,65,280 ways for this selection.

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