Question

hell I'm stuck one this problem and need help ty

Answer 1

(a) If the order is relevant, then we need to calculate the number of permutations.

The number of permutations of n things chosen r at a time is found using:

$_nP_r=\frac{n!}{(n-r)!}$

In this case, we want to choose r = 3 colors, from a total of n = 4 colors. Using these values in the above formula, we get:

$_4P_3=\frac{4!}{(4-3)!}=\frac{4!}{1!}=\frac{24}{1}=24$

(b) If the order is not relevant, then we need to calculate the number of combinations.

The number of combinations of n things chosen r at a time is found using:

$_nC_r=\frac{n!}{r!(n-r)!}$

In this case, we want to choose r = 3 colors, from a total of n = 4 colors. Using these values in the above formula, we get:

$_4C_3=\frac{4!}{3!(4-3)!}=\frac{4!}{3!\cdot1!}=\frac{24}{6\cdot1}=4$