SOLUTION: Hi tutors at algebra.com, <p> I have this question and its difficult. It has some connection with probability and thats what I know, and with a bit of chance and finding out var

Algebra ->  Probability-and-statistics -> SOLUTION: Hi tutors at algebra.com, <p> I have this question and its difficult. It has some connection with probability and thats what I know, and with a bit of chance and finding out var      Log On


   

Question 131195: Hi tutors at algebra.com,


I have this question and its difficult. It has some connection with probability and thats what I know, and with a bit of chance and finding out various probabilities, etc..but I'm not sure how you can work it. I've tried thinking of it the number of ways, but its different from the correct answer that I was given, which was 20. If you could explain to me how you got the answer I would really appreciate it. Here's the question:


"In the school band 5 children each own their own trumpet. In how many different ways can exactly three of the five children take home the wrong trumpet, while the other two take home the right trumpet."


Any help and an explanation would be appreicated. Thankyou so much, Jasmine (13 years old)
Answer by edjones(8007) About Me  (Show Source):

You can put this solution on YOUR website!
We want to know the different Combinations of 3 of the 5 kids there can be.
n=5, r=3,
nCr=n%21%2F%28%28n-r%29%21%2Ar%21%29
5C3=5%21%2F%28%285-3%29%21%2A3%21%29
=%285%2A4%2A3%2A2%2A1%29%2F%28%282%2A1%29%283%2A2%2A1%29%29
=%285%2A4%29%2F2
=10 different ways
.
Ed