Question

Evaluate each of the following. (a) P(11,5) (b) C(11,5) (a) P(11,5) = (Simplify your answer.) (b) C(11,5) = (Simplify your answer.) 7/3 072 07/3 Enter your answer in each of the answer boxes 11:34

Answer 1

Answer:

(a)   P(11,5)= 55440

(b)  C(11,5)=462

Step-by-step explanation:

We know that the permutation is the number of ways of arranging r items out of a total of n items and is given by:

$P(n,r)=\dfrac{n!}{(n-r)!}$

and the combination is the number of ways of choosing r items out of a total of n items and is given by:

$C(n,r)=\dfrac{n!}{r!\times (n-r)!}$

(a)

               P(11,5)

$P(11,5)=\dfrac{11!}{(11-5)!}\\\\P(11,5)=\dfrac{11!}{6!}\\\\P(11,5)=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{6!}\\\\P(11,5)=11\times 10\times 9\times 8\times 7\\\\P(11,5)=55440$

(b)

                 C(11,5)    

$C(11,5)=\dfrac{11!}{5!\times (11-5)!}\\\\C(11,5)=\dfrac{11!}{5!\times 6!}\\\\C(11,5)=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{5\times 4\times 3\times 2\times 1\times 6!}\\\\C(11,5)=462$