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

(a) P(11,5)= 55440

(b) C(11,5)=462

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)=(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)=(n!)/(r!* (n-r)!)`

(a)

P(11,5)

`P(11,5)=(11!)/((11-5)!)\\\\P(11,5)=(11!)/(6!)\\\\P(11,5)=(11* 10* 9* 8* 7* 6!)/(6!)\\\\P(11,5)=11* 10* 9* 8* 7\\\\P(11,5)=55440`

(b)

C(11,5)

`C(11,5)=(11!)/(5!* (11-5)!)\\\\C(11,5)=(11!)/(5!* 6!)\\\\C(11,5)=(11* 10* 9* 8* 7* 6!)/(5* 4* 3* 2* 1* 6!)\\\\C(11,5)=462`