THANKS A TON!!! I’m taking trigonometry at school, and I couldn’t even follow along during these past few lessons because I didn’t understand anything. Your website is extremely helpful 
THANK YOU!!
Very helpful. Thank you for this site. I’m in seventh grade and even for me it is very clear. Thanks again
@Jackson: “B” will refer to boys and “G” to girls
As far as I can understand, this is a permutation. Hence order IS important. 2 types of orders are possible in this condition; Starting with a boys or starting with a girl
Consider a Boy/Girl situation.
Order: B G B G B G B G => 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1 = 4! x 4!
Consider a Girl/Boy situation:
Order: G B G B G B G B => 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1 = 4! x 4!
====> Total ways: (4! x 4!) + (4! x 4!) = 2(4! x 4!) = 1152 ways
This is based solely on my understanding. I’m a student myself and might have made mistake(s). Thanks
There a four boys and four girls .In how many ways can they form a line, with the boys and girls alternating?
Thank you, thank you, thank you!
I’ve been banging my head against this problem at Khan Academy for a week and was finally able to work through it. Understanding the “why” of things really helps.
very useful infact
Hi. This site really helped me a lot. Thank you so much, Kalid.
i have 5 positive signs and 3 negative signs i want arrange them in such way that the negative never come together?
This is soo useful to understand at a very short time…thank u soo much…
After practicing for hours and hours, I finally understood the difference. This was great help!
if u pick a ball from 6red and 4 blue &
4 red and 5 blue what is the probability to get one red and another blue?
ASKED IN RBI GRADE B
Great article. The explanation of combinations was brilliantly explained. Thanks.
@Khalid: Could the explanation for #comment 30 also be given as:
No:of ways of selecting 1 question(6C1) + no:of ways of selecting 2 questions (6C2)+…+no:of ways of selecting all questions(6C6). I get the same answer (63 excluding 0) when I add them up
Also,why do we learn permutations first and then derive for combinations all the time, can’t it be taught the other way round?
Hi Kalid,
I have a question. I understand that the combination for getting 3 balls from 10 balls is 120. Could you please let me know the formula if the user is given 4 chances to pick 3 balls out of 10 balls.
Thanks
I have 7 tennis players, 38 weeks of tennis time, 4 players each week. Is it possible to schedule so that each player has equal number of days off and is scheduled to play with every player?
This is incredibly helpful. I am studying for the GRE and, even with one graduate degree under my belt already, I have very little math background. Many of the quantitative reasoning questions are related to combinations and permutations and, although I had memorized the formulas, I was having a very difficult time applying them quickly and effectively, and I certainly wasn’t able to REASON well. This explanation helped me easily understand the reasoning behind the formulas and I am now able to quickly apply them where appropriate and solve problems much more efficiently. I particularly appreciated the use of humor in the delivery of these explanations. Humor is an excellent and underutilized learning and memory tool!!
Please explain the difference -which is a combination and which is a permutation of these two problems - I just don’t get it. Each assumes a standard 52 card deck.
- How many different ways can you deal out 5 cards?
- How many different 5 card hands exist?
fire brigade mangwale tu…angaro par hai aarma…o balma o balma…
really very useful…thanks a lot