# Thread: Question relating to Permutations and Combinations...

1. ## Question relating to Permutations and Combinations...

Hey I was wondering if anyone could help me solve this problem->

A) If Peg has 4 long-sleeve shirts, 5 short-sleeve shirts, and 4 pairs of pants, how many different ways can she dress (assuming she is going to wear a shirt and pants)?

B) If she is going on a trip and plans to take 3 shirts and 2 pairs of pants, how many possibilities are there for the articles of clothing she chooses?

C) Same as the previous question, except she decides that the shirts she takes should all be long sleeve?

D) How many possibilities would there be if instead of deciding the shirts should ALL be long sleeve she decides that she should take AT LEAST ONE long sleeve shirt?

I got the answer to the first question by simply multiplying the number of shirts and pants which gave me 36.
I also found the answer to the second question by doing
(9!/3!*6!) * (4!/2!*2!) = 504
I solved the third problem by doing (4!/3!) * (4!/2!*2!) = 24

...But I'm stuck on the last problem =/ can anyone help me??

Thank you!!

2. ## Another problem

I was having difficulties with this one as well->

A combination lock shows 30 different numbers on the dial. To open the lock, the user must know the three-number sequence that is the "combination" for the lock. For example, to open the lock one might have to dial the three numbers 12-2-14 in the order shown here (first dialing 12, then 2, then 14). In a combination, you can't have two consecutive numbers that are the same. For example, you can have 7-10-7 but you can't have 7-7-10.

How many different combinations are possible?