## arindameducationusc one year ago Challenge and also a help..... Check image for question

1. arindameducationusc

2. arindameducationusc

3. arindameducationusc

4. ganeshie8

look at the 10th row in pascal's triangle : |dw:1438086192297:dw|

5. ganeshie8

We want to find $$x$$ such that $\large ^{10}C_{x-1} - 3 *^{10}C_{x}~\gt~ 0$

6. arindameducationusc

yes i m looking

7. ganeshie8

|dw:1438086392992:dw|

8. arindameducationusc

yes >0 , understood that because sqare root function and denominator

9. ganeshie8

notice that 45-3*10 > 0 10-3*1 > 0 1 - 3*0 > 0 so, x = 9, 10, 11 are fine

10. arindameducationusc

The answer is none of these... so I am confused

11. ganeshie8

x = 8 doesn't work because 120 - 3*45 < 0 similarly x>11 doesn't work because 0 - 3*0 = 0

12. ganeshie8

answer is $$a$$ to my knowledge

13. arindameducationusc

let me analyse once, give me some time then I may ask you if you have no problem @ganeshie8

14. ganeshie8

sure

15. ganeshie8
16. arindameducationusc

Is this the language for combinations? Thats interesting.... hmmm...

17. arindameducationusc

solve (10 choose (x-1)) - 3*(10 choose x) > 0 over integers Can you explain this sentence with respect ot combination?

18. arindameducationusc

#to#

19. ganeshie8

$$\large ^nC_r$$ is read as $$\large n~~\text{choose}~~r$$

20. ganeshie8

it is called binomial coefficient and represented by symbol : $\large \binom{n}{r}$

21. arindameducationusc

Each of the different groups or selections which can be made by taking some or all of a number of things(irrespective of order) //Can you please elaborate this sentence

22. arindameducationusc

// Its for Combination

23. arindameducationusc

45-3*10 > 0 You checked this for 9?

24. ganeshie8

yes that is for x = 9

25. ganeshie8

suppose you went for shopping and liked 5 shirts

26. arindameducationusc

ok

27. ganeshie8

but you can only buy 3 of them

28. arindameducationusc

ok

29. ganeshie8

how many ways are there to choose 3 shirts from the 5 shirts ?

30. ganeshie8

for definiteness, lets call the shirts : $$a,~b,~c,~d,~e$$

31. arindameducationusc

calculations say 10

32. ganeshie8

can you list them all ?

33. arindameducationusc

ok go on... nice

34. arindameducationusc

no, I don't have that strong concept.... I would definitely understand from you.... nice....

35. ganeshie8

no, just list them all, its a simple counting problem

36. ganeshie8

you can buy the shirts $$a,b,c$$ or $$b,c,d$$ or $$c,d,e$$ or ... try listing them all

37. arindameducationusc

okay ... abc acd bed bcd ade bec cde aeb

38. arindameducationusc

more two

39. ganeshie8

looks two are missing yeah

40. arindameducationusc

I am trying :P

41. arindameducationusc

bae

42. arindameducationusc

no no not bae

43. ganeshie8

 {a,b,c} {a,b,d} {a,c,d} {b,c,d} {a,b,e} {a,c,e} {b,c,e} {a,d,e} {b,d,e} {c,d,e} 

44. ganeshie8

$$\large ^{5}C_3$$ gives the number of ways you can choose 3 shirts from 5

45. arindameducationusc

Thank you.... any method to find the terms in order... like you easily sound out the 10. suppose 16 or 24... any trick is there?

46. arindameducationusc

##found##

47. ganeshie8

i hope you're familiar with the formula for computing $$^5C_3$$ : $^5C_3 = \dfrac{5!}{3!(5-3)!} =\dfrac{5!}{3!*2!}= \dfrac{5\times 4\times 3\times 2\times 1}{3\times 2\times 1*2\times 1} = 10$

48. arindameducationusc

yes yes.... ofcourse

49. arindameducationusc

I am talking about counting.. thats hard! :P

50. ganeshie8

Thank you.... any method to find the terms in order... like you easily sound out the 10. suppose 16 or 24... any trick is there? hey i didnt get what you're asking..

51. arindameducationusc

suppose abcdefgh and we have to choose 3 pairs then is there any way by counting? Like suppose I want to view all possibilities

52. ganeshie8

you want see the entire list of 56 choices ?  {a,b,c} {a,b,d} {a,c,d} {b,c,d} {a,b,e} {a,c,e} {b,c,e} {a,d,e} {b,d,e} {c,d,e} {a,b,f} {a,c,f} {b,c,f} {a,d,f} {b,d,f} {c,d,f} {a,e,f} {b,e,f} {c,e,f} {d,e,f} {a,b,g} {a,c,g} {b,c,g} {a,d,g} {b,d,g} {c,d,g} {a,e,g} {b,e,g} {c,e,g} {d,e,g} {a,f,g} {b,f,g} {c,f,g} {d,f,g} {e,f,g} {a,b,h} {a,c,h} {b,c,h} {a,d,h} {b,d,h} {c,d,h} {a,e,h} {b,e,h} {c,e,h} {d,e,h} {a,f,h} {b,f,h} {c,f,h} {d,f,h} {e,f,h} {a,g,h} {b,g,h} {c,g,h} {d,g,h} {e,g,h} {f,g,h} 

53. ganeshie8

as you can see its not so pleasant to list them all... why would you want to do that lol

54. arindameducationusc

ofcourse it is unpleasant! but Maths is Maths.... but can you tell me how did you do it?

55. arindameducationusc

Can Wolfram do this?

56. ganeshie8
57. arindameducationusc

Thank you so much for giving your precious time.... :)

58. ganeshie8

comb(n, set) lists all the combinations of size "n" from the set "set"

59. ganeshie8

but trust me, you almost never want to list all the possibilities in math most of the time you only want the total number of choices, not the list.

60. arindameducationusc

ya its working.... thank you....

61. arindameducationusc

Ok got it! :P