Suppose we want to choose 5 colors, without replacement, from 16 distinct colors.

Complete question is;

Suppose we want to choose 5 colors, without replacement, from 16 distinct colors.

A) How many ways can this be done, if the order of the choices is taken into consideration?

B) How many ways can this be done, if the order of the choices is not taken into consideration?

A) 524160 ways

B) 4368 ways

Step-by-step explanation:

A) If the order of choices is taken into consideration, then it is a Permutation problem.

Formula for Permutation is;

P(n, r) = n!/(n - r)!

In the question, n = 16 and r = 5

Thus;

P(16, 5) = 16!/(16 - 5)!

P(16, 5) = 524160

B) If the order of choices is not taken into consideration, then it becomes a Permutation problem.

Formula for Combination is;

C(n, r) = n!/((r! × (n - r)!)

C(16, 5) = 16!/((5! × (16 - 5)!)

C(16, 5) = 4368

46.2+112.3

step-by-step explanation:

so, converting firstly the mixed fractions to improper fractions and then "adding".