Alawyer owns 4 pairs of pants, 5 dress shirts and 6 ties. how many days can the lawyer go without wearing the same combination of three items?

4 × 5 × 6 = 120

Explanation:

1) This is a direct use of the counting principle, which states that the number of different ways a combination of independent events can happen is equal to the product of the number of different outcomes for each event.

That is, if event A can have m different outcomes, event B can have n different outcomes, and event C can have p different outcomes, the total number of different combinations is m × n × p.

2) In this case, the lawyer can use 4 different pais of pants, 5 different shirts, and 6 different ties, so the number of different combinations of the three items is: 4 × 5 × 6 = 120.

3) You can see that if you make a diagram (may be a tree diagram).

With that you can see that each pair of pants, can go with 5 shirts, which make 4 × 5 different couples of pants - shirts. After that, each different couple of pants - shirts can go with 6 different ties, so you have 4 × 5 × 6 three-piece combinations.

answer: the correct answer is -32

step-by-step explanation: