Can someone help me with these questions? My math book IMO sucks and the wording is really poor at times.
1. How many ways can five different pairs of identical teddy bears be arranged in two rows of five for a photograph?
I tried solving this. However, I honestly don't even know what this is even asking.
I know you use permutations to solve, because order matters, right? I tried doing 10 P 5 X 5 P 5 but no luck. I assumed there were 10 bears in total, but IDK.
The answer is 113,400. I don't know how they got this.
2. Six different types of boats have pulled into a marina and want to dock at the six available slips. The six slips are adjacent to each other. How many ways can the six boats dock so that two cabin cruisers, which are travelling together, are docked next to each other?
The answer apparently is 240. I tried a lot of different solutions but nothings working.
3. How many different five-card hands that contain at most three hearts can be dealt from a standard deck of playing cards?
I think I am close to the solution here. I know what you have to do technically. I considered 4 separate cases:
0 hearts, 5 other suits
1 heart, 4 other suits,
2 hearts, 3 other suits,
3 hearts, 2 other suits
I know this is a combinations problem. I just don't know what my N values would be.
Like to solve, I thought:
13 C 0 X 39 C 5 + Case 2 + Case 3+Case 4...etc
but I am off by a lot. The answer is 2,569,788. Again IDK how they got this.