Question

Suppose we want to choose 6 colors, without replacement, from 12 distinct colors.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 order pf the choices is NOT relevant

Answer 1

To choose 6 colors without replacement, there are 665,280 ways if the order is relevant and 924 ways if the order is not relevant.

Step-by-step explanation:

To solve this problem, we can use combinations to calculate the number of ways to choose colors without replacement.

A) If the order of the choices is relevant, we can use the formula for permutations: P(n,r) = n! / (n-r)!. In this case, we want to choose 6 colors from 12, so the number of ways is P(12,6) = 12! / (12-6)! = 12! / 6! = 665,280 ways.

B) If the order of the choices is not relevant, we can use the formula for combinations: C(n,r) = n! / (r!(n-r)!). In this case, we want to choose 6 colors from 12, so the number of ways is C(12,6) = 12! / (6!(12-6)!) = 12! / (6!6!) = 924 ways.