Suppose we want to choose colors, without replacement, from the colors red, blue, green, and purple.

(a) How many ways can this be done, if the order of the choices is relevant?

(b) How many ways can this be done, if the order of the choices is not relevant?

Respuesta :

The number of ways when the choice is not relevant is 4

How to determine the number of ways?

The number of colors are:

Colors, n = 4

The color to choose are:

r = 3

Relevant choice

When the choice is relevant, we have:

[tex]Ways = ^nP_r[/tex]

This gives

[tex]Ways = ^4P_3[/tex]

Evaluate

Ways = 24

Hence, the number of ways when the choice is relevant is 24

Not relevant choice

When the choice is not relevant, we have:

[tex]Ways = ^nC_r[/tex]

This gives

[tex]Ways = ^4C_3[/tex]

Evaluate

Ways = 4

Hence, the number of ways when the choice is not relevant is 4

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