Question

Use the permutation formula to solve a problem when n = 15 and r = 4.



A.
B. 54
C. 3,276
D. 32,760

Answer 1

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

$15P4 = \frac{15!}{(15 - 4)!} = \frac{15!}{11!} \\ = \frac{15 \times 14 \times 13 \times 12 \times 11!}{11!} \\ 15 \times 14 \times 13 \times 12 = 32760$

Answer 2

The permutation of the given values will be $32,760$.

What is permutation ?

A permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.

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

We have,

$n = 15$

And

$r = 4$

So, using Permutation Formula;

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

i.e.

$^nP_{r}= \frac{15!}{(15-4)!}$

      $= \frac{15!}{11!}= \frac{15*14*13*12*11!}{11!}$

Now, cancelling factorial terms,

We get,

$^nP_{r}= 15*14*13*12$

$^nP_{r} =32760$

So, the value is $32760$.

Hence, we can say that the permutation of the given values will be $32,760$.

To know more about Permutation click here

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