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=(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=(4!)/((4-3)!)=(4!)/(1!)=(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=(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=(4!)/(3!(4-3)!)=(4!)/(3!\cdot1!)=(24)/(6\cdot1)=4`