Determine the number of ways in which 8 people can be divided into 2 equal groups.

Question

anonymous · Answer

Hint: You need to pick 4 people from 8. Combination problem.

lgbasallote · Answer

dont you just use combinations?

$$nCr = \frac{n!}{r!(n-r)!}$$
$$8C2 = \frac{8!}{2!(8-2)!}$$

anonymous · Answer

uh why do you need to pick 4 people from 8?

anonymous · Answer

2 Equal groups. How many people will be there in one group 4 right?

anonymous · Answer

yeh

anonymous · Answer

Now you need to select 4 out of 8.

anonymous · Answer

but 8 people right? and we want two groups? so 4 people in one group but you only pick one or...?

anonymous · Answer

so confusing....

anonymous · Answer

Nope. How many people you need to pick? Equal groups means 4 +4. So you will pick 4 out of eight to make a group. In 8C4 ways you can pick 4 people from 8 right?. What's confusing?

anonymous · Answer

It doesn't say how many people to pick or anything just basically how many groups we can divide evenly?

anonymous · Answer

oh k, I think I got it now, don't worry.

anonymous · Answer

Okay let's say A B C D E F G H are 8 persons. How many ways you can divide equally? 

( A B C D) ( E F G H) + ( A B C E) (D F G H)+ and so on right? Unknowingly you are picking right

anonymous · Answer

yeh.

anonymous · Answer

Mathematically we will write 8C4 right?

anonymous · Answer

yep.

anonymous · Answer

I get it now, but can you help me with this last example.

anonymous · Answer

The number of ways in which 10 objects can be divided into 2 unequal groups is:

A 385

B 835

C 950

D 640

E 565

anonymous · Answer

I think it's something - 10C5

rsadhvika · Answer

tough one

rsadhvika · Answer

10C1 + 10C2 + ........ 10C10 - 10C5


assuming a group can have 0 objects

rsadhvika · Answer

each term represents number of ways to chose objects for first group

anonymous · Answer

but there's no answer for that.

anonymous · Answer

the answer for the way u did it @rsadhvika is 771 and there's no option for that.

rsadhvika · Answer

2(1+10+45+120+210)

it cannot be a odd number

rsadhvika · Answer

772

rsadhvika · Answer

ok its not there in the options either

anonymous · Answer

ok well it's late over here so I got to sleep now, if you can get the answer just show me the working, thanks.

anonymous · Answer

I'm litle bc. I'll try this later..:)