The following shows the distribution of players in a soccer team.
Position | Number of players
-------------------------
Goalkeeper | 3
Defender | 8
Midfielder | 6
Forward | 5

Q: To start a game, 11 players including 1 goalkeeper are selected.
Suggest how to select the 11 players if the number of choices is
(a) grater than 25000;
(b) grater than 35000.

Question

The following shows the distribution of players in a soccer team.
Position | Number of players
-------------------------
Goalkeeper | 3
Defender | 8
Midfielder | 6
Forward | 5

Q: To start a game, 11 players including 1 goalkeeper are selected.
Suggest how to select the 11 players if the number of choices is 
(a) grater than 25000;
(b) grater than 35000.

anonymous · Answer

@ganeshie8

anonymous · Answer

@amistre64 @nubeer

amistre64 · Answer

$$\binom{3}{1}\binom{8}{a}\binom{6}{b}\binom{5}{c}$$
such that a+b+c = 11

anonymous · Answer

yeah i know

amistre64 · Answer

is including 1, retricted to 1? or does it mean "at least 1

anonymous · Answer

including

amistre64 · Answer

hmmm
$$\frac{3!~8!~6!~5!}{a!(8-a)!~b!~(6-b)!~c!(5-c)!}$$
well that doesnt seem to help out lol

anonymous · Answer

too complicated i think.

amistre64 · Answer

yeah .... im wondering if there is a simpler way to setup an inequailty;  or a simple way to trial and error it

anonymous · Answer

the topic mainly focus on permutation and combination...

amistre64 · Answer

i would hope so :)

anonymous · Answer

by the way, this is an open-ended question..

amistre64 · Answer

25000/3 to narrow the field (assuming we only get to pick one goalee)

anonymous · Answer

wow, i hate this type of questions..

amistre64 · Answer

3 8 6 5 = 42000
1 4 3 3

anonymous · Answer

you got the answer 1, 4, 3, 3 for the part b....
i am wondering what your steps are...

amistre64 · Answer

3 8 6 5 = 25 200
1 3 4 3

amistre64 · Answer

trial and error :)

anonymous · Answer

part a, 1, 4, 4, 2
part b, 1, 4, 3, 3

but i think my teacher will not recommend us to use trial and error..

amistre64 · Answer

trial and error is the staple of mathematical figurings ...

amistre64 · Answer

1,4,4,2 is 31500,  i like my 1,3,4,3 better since its closer to 25000 for a

anonymous · Answer

i think your ideas are also okay as the question is open-ended

amistre64 · Answer

if we line them up as:

3 5 6 8,  we have the possibilities of
1 0 2 8
1 0 3 7
1 0 4 6
1 0 5 5
1 0 6 4
1 1 2 7
1 1 3 6
etc .... which can be run in a search algorithm

anonymous · Answer

is it simply sub the number and make the inequality greater than 25000 and 35000?

anonymous · Answer

wow

amistre64 · Answer

i assumed a and b are two seperate events

anonymous · Answer

what?

amistre64 · Answer

thats a possible setup yes; but i see know way of simplifying it other than a trial and error run.  I just aint that smartical ;)

anonymous · Answer

wow, thank you very much :)

amistre64 · Answer

youre welcome, and good luck