Combinations - selecting 7 persons

1. Sep 3, 2010

rajatgl16

In how many ways 7 persons can be selected from 5 indian, 4 british and 2 chinise, if atleast 2 are to be selected from each country.

2. Sep 3, 2010

rpf_rr

Re: Combination

you have to choose two chinese forced, at least two british and two indians, and one between british or indian. so you have

1*$$\frac{4!}{2!2!}$$*$$\frac{4!}{2!2!}$$*(3+2)=180

the last term: 3 indians+2 british

Last edited: Sep 3, 2010
3. Sep 4, 2010

rajatgl16

Re: Combination

hey I have answer booklet (not solution). And in it answer given is "100".

I tried it as,
At least 2 persons have to be slected form each country so :

ways of selecting 2 persons from 5 indians is 5C2

ways of selecting 2 persons from 4 british is 4C2

ways of selecting 2 persons from 2 chinese is 2C2

Thus ways of slecting 6 persons form entire group is 5C2 * 4C2 * 2C2

Now 1 person has to be selected from remaing 3 Indians and 2 british and 0 chinese

possible way of selceting 1 person is 5C1

Thus final answer to select 7 persons is 5C2 * 4C2* 2C2 * 5C1=300 so its also wrong

4. Sep 4, 2010

rpf_rr

Re: Combination

for nCk you mean n!/(k!*(n-k)!) ? If yes we computed the same thing, or better, you are right, i've done an error in the third factor, it is actually 5C2=5!/(3!2!), for me it's 600, but i made the same reasoning as you did, and i think it's right, if we understand the problem correctly.

5. Sep 4, 2010

rajatgl16

Re: Combination

Then may be ans in my ans booklet is wrong.

6. Sep 4, 2010

Office_Shredder

Staff Emeritus
Re: Combination

You've overcounted some. Imagine the British people are labeled A,B,C and D.

Scenario 1: You pick two British, A and B. Then you pick two Indians. Then you pick your last person from the five remaining people and pick person C.

Now imagine instead you pick two British, A and C. You pick the same two Indians as before. You pick your last person from the five remaining people and the person is B.

In both situations you've picked the same set of people but you counted them separately

7. Sep 4, 2010

rpf_rr

Re: Combination

Officeshredder is right. There are two possible situations, you pick 2 chinese 3 british and 2 indians or you pick 2 chinese 2 british and 3 indians, so you have
2C2*4C3*5C2+2C2*4C2*5C3=100

8. Sep 4, 2010

rajatgl16

Re: Combination

Hmm. I was wrong. Thanks guys for helping me,