How Many Ways Can an 8 Oar Boat Crew Be Selected from 11 People?

In summary, the problem is to select a crew of 8 from a group of 11 people, with 5 only able to oar on one side, 4 only able to oar on the other side, and 2 able to oar on either side. The three possibilities are to have 7 on one side and 4 on the other, 6 on one side and 5 on the other, or 5 on one side and 6 on the other. The solution is to select 4 people for the right side and 4 people for the left side to maintain equal strength on either side of the boat.
  • #1
xiphoid
57
0

Homework Statement


A crew of an 8 oar boat has to be selected from 11 people, out of which 5 can oar only on one side, 4 can oar only on the other side and 2 can oar on either sides, find in how many ways can the selection be done?



The Attempt at a Solution



What I did here is assumed 3 possibilities
1. 7 on one side and 4 on the other---- assuming those two to be on one side
2. 6 on one side and 5 on the other---- equally dividing them on each side
3. 5 on one side and 6 on the other---- equally dividing them on each side
 
Physics news on Phys.org
  • #2
In Oaring a boat, you have to man equal strength on either side or the boat will no go straight. Here, select 4 people for right side and 4 people for left side.
 

What is the difference between permutation and combination?

Permutation and combination are both mathematical concepts used to count and arrange objects. However, permutation refers to the arrangement of objects in a specific order, while combination refers to the selection of objects without regard to order.

How do I calculate the total number of possible permutations?

To calculate the total number of possible permutations, you can use the formula n! / (n-r)! where n represents the total number of objects and r represents the number of objects being selected or arranged. For example, if you have 5 objects and you want to arrange 3 of them, the formula would be 5! / (5-3)! = 5! / 2! = 60 possible permutations.

What is the formula for calculating combinations?

The formula for calculating combinations is n! / r!(n-r)! where n represents the total number of objects and r represents the number of objects being selected. For example, if you have 5 objects and you want to select 3 of them, the formula would be 5! / 3!(5-3)! = 5! / (3!)(2!) = 10 possible combinations.

When do I use permutation and when do I use combination?

You would use permutation when you want to calculate the total number of possible arrangements of objects in a specific order. Combination, on the other hand, is used when you want to calculate the total number of ways to select a certain number of objects without regard to order.

What are some real-life applications of permutation and combination?

Permutation and combination have various applications in fields such as mathematics, statistics, computer science, and economics. Some real-life examples include calculating the possible seating arrangements at a dinner party, finding the number of possible outcomes in a game of cards, and predicting the chances of winning a lottery or raffle.

Similar threads

Probability of selecting two white balls from two bags
    • Precalculus Mathematics Homework Help
Replies
2
Views
1K
Arrange 4 Guests on One Side: 9C4*4!*9C3*3!*11!
    • Precalculus Mathematics Homework Help
Replies
24
Views
2K
MHB Finding 2D Polygon Coordinates from a point
    • General Math
Replies
2
Views
1K
MHB #s of Combinations and Permutations of lines?
    • General Math
Replies
1
Views
719
I Orbitals and selection rules in a synchrotron
    • Quantum Physics
Replies
18
Views
1K
I Probability to get a certain number or less by throwing two 6-faced die
    • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
Probability Questions: Union, Intersection and Combinations
    • Calculus and Beyond Homework Help
Replies
16
Views
1K
Writing: Input Wanted Civilians in Space vs. Professionalism and Military Decorum
    • Sci-Fi Writing and World Building
Replies
7
Views
1K
Permutations - arrangement of a boat crew of 8 women
    • Precalculus Mathematics Homework Help
Replies
3
Views
3K
B Logic Problem: Figuring Out How Many Apples Each Man Ate
    • Set Theory, Logic, Probability, Statistics
Replies
9
Views
569

Hot Threads

Recent Insights

Back
Top