Question

Which of the following is NOT a requirement of the Combinations​ Rule, Subscript n Baseline Upper C Subscript requalsStartFraction n exclamation mark Over r exclamation mark left parenthesis n minus r right parenthesis exclamation mark EndFraction ​, for items that are all​ different? Choose the correct answer below. A. That r of the n items are selected​ (without replacement). B. That there be n different items available. C. That order is not taken into account​ (consider rearrangements of the same items to be the​ same). D. That order is taken into account​ (consider rearrangements of the same items to be different​ sequences).

Answer 1

Answer:

C. That order is taken into account

Answer 2

Answer:

D. That order is taken into account​ (consider rearrangements of the same items to be different​ sequences).

Step-by-step explanation:

$C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

For example:

Combinations of 2 from a set a,b,c: ab=ba, ac = ca, bc = cb, meaning that the order is not important(ab and ba is the same sequence).

aa, bb, cc are not valid, since there is no replacement.

So the answer for this qustion is:

D. That order is taken into account​ (consider rearrangements of the same items to be different​ sequences).