About Chanda Walker Expertise I can answer word problems involving mathematics at the high school and college level. I particularly enjoy calculus word problems. Please don't just type the math problem without comments. If you don't tell me what problem your having, I can't help.
Experience Have done word problems as a tutor and as a student of mathematics and physics for years.
Organizations Sigma Xi
Education/Credentials Optical Science PhD
Past/Present Clients I've answered hundreds of questions here at AllExperts.com in algebra, physics and general math sections.
Question QUESTION: There is a lottery where there are 5 numbers drawn out of 45. You have the
option of picking 7, 9, and 10 numbers out of which you only need to match the
5 drawn numbers. What are your chances of winning, when you choose 7, 9 or
10 numbers. (Numbers are drawn from 1-45). Thanks
ANSWER: The way I think about this is that there are 5 red balls and 40 blue balls in a bag. The red balls represent the 5 winning lottery numbers. You want to draw ALL 5 out of the bag. You get to pick draw 7, 9 or 10 numbers.
Choose 7:
The number of ways to pick 5 red and 2 blue:
5C5 * 40C2 = 1 * 780
The number of ways to pick 7 out of 45 is:
45C7 = 45379620
The ratio of these are: 1/58179 or ~0.000017
******************
Choose 9:
The number of ways to pick 5 red and 4 blue:
5C5 *40C4 = 91390
The number of ways to pick 9 out of 45 is:
886163135
The ratio:
2/19393
**********************
Choose 10:
5 red and 5 blue:
658008
10 out of 45:
3190187286
The ratio:
4/19393
If you don't understand the 40C4 notation, just let me know and I'll explain that fully.
---------- FOLLOW-UP ----------
QUESTION: Thanks for the reply.
Firstly, yes I do need you to explain to me the 40C4 notation and secondly I
don't understand your response, when you say 2/19393 is that 1/9,696.5 or
~0.000103 and the same for choosing 10 and needing only 5 of these to win?
Thanks
Answer 40C4 is said: 40 choose 4
This is standard notation for permutation and combinations.
nCk (n choose k) has a numerical formula of:
n!/((n-k)!k!)
In case you don't know what the ! is . . . that is called a factorial and I'll give you an example:
5! is 5*4*3*2*1
You just multiply all the integers starting from the number given down to one. Another example:
7! = 7*6*5*4*3*2*1
When I say 2/19393 I mean the fraction of 2 divided by 19393. I didn't divide that out all the way since I assumed you had a calculator handy.
Let me know if it still doesn't make sense. If you want more fundamental understanding of what is going on, just let me know. I never know how deeply one wants me to explain things when they only type the question. If you want me to explain the concept, I can and I'm happy to do so.
