Q

# Try this! The number of ways in which 12 balls can be divided between two friends, one receiving 8 and the other 4, is:

The number of ways in which 12 balls can be divided between two friends, one receiving 8 and the other 4, is:

• Option 1)

$\frac{12!}{8!4!}$

• Option 2)

$\frac{12!2!}{8!4!}$

• Option 3)

$\frac{12!}{8!4!2!}$

• Option 4)

None of these

137 Views

As learnt in concept

Rule for Division into Groups -

The number of ways in which (m + n) different things can be divided into two groups which contain m and n things respectively is $\frac{(m+n)!}{m!\ n!}$.

-

grouping ways are $\frac{12!}{8!4!}$
now they can be done in any way

So,

$\frac{12!}{8!4!}\times 2!$

Option 1)

$\frac{12!}{8!4!}$

This is incorrect option

Option 2)

$\frac{12!2!}{8!4!}$

This is correct option

Option 3)

$\frac{12!}{8!4!2!}$

This is incorrect option

Option 4)

None of these

This is incorrect option

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