Question

Answer the following questions. 

Describe how the permutation of n objects differs from the permutation of choosing r objects from a set of n objects. Include how each is calculated.

Answer 1

Permutation of n objects is the number of ways to arrange the n objects in order. Permutation of n distinct objects is written as P(n, n) and is calculated by following formula,

P(n, n) = n!

 

For example:

A play has a cast of 7 actors to make their curtain call. 7 actors are lining up for the curtain call.

Substitute n = 7 in formula for permutations of n distinct objects,

P(7, 7) = 7!

            = 5040

 

So, total number of possible ways 7 actors can line up for the curtain call is5040.

 

Permutation of choosing r objects from a set of n objects is the number of ways to choose r objects from the given n objects and arrange them in order. Permutation of choosing r objects from a set of n objects is written as P(n, r) and is calculated by following formula,

P(n, r) = n!/(n – r)!

 

For example:

A play has a cast of 7 actors to make their curtain call. 5 out of 7 actors are to be chosen form line up.

Substitute n = 7 and r = 5 in formula for permutations of choosing r objects from a set of n objects,

P(7, 5) = 7!/(7 – 5)!

            = 7!/2!

           = (7 × 6 × 5 × 4 × 3 × 2 × 1)/2!

           = 2520

 

So, 5 out of 7 actors can be chosen in 2520 ways to line up.

So, 5 out of 7 actors can be chosen in 2520 ways to line up.