Question

Which of the following is NOT a requirement of the Combinationsâ Rule, Subscript n Baseline Upper C Subscript requalsStartFraction n exclamation mark Over r exclamation mark (n minus r )exclamation mark EndFraction â, for items that are allâ different?
a. That r of the n items are selectedâ (without replacement).
b. That there be n different items available.
c. That order is not taken into accountâ (consider rearrangements of the same items to be theâ same).
d. That order is taken into accountâ (consider rearrangements of the same items to be differentâ sequences).

Answer 1

Answer:

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

Step-by-step explanation:

Given the combination rule:

$^nC_r=\dfrac{n!}{r!(n-r)!}$

A major difference between permutation and combination is the order of the items in the selection. If the order does not matter then we have a combination. If on the other hand, the order of the items matter, then it is a permutation.

Therefore, that which is not a rule for combination is Option D since, in combination, we do not consider rearrangements of the same items to be different sequences.