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  4. Number of ways in which 5 alike red balls and 6 alike green balls can be arranged so that exactly two pairs of green balls are together and separated from each other, is

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Q. Number of ways in which 5 alike red balls and 6 alike green balls can be arranged so that exactly two pairs of green balls are together and separated from each other, is

Permutations and Combinations

Solution:

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$\&$ selection of 2 more gaps from the remaining 4 in ${ }^4 C_2$ ways for $G$ and $G$
$\therefore $ Total ways $={ }^6 C _2 \cdot{ }^4 C _2=\frac{6 !}{2 ! 4 !} \cdot \frac{4 !}{2 ! 2 !}=\frac{6 !}{2 ! 2 ! 2 !}=\frac{720}{8}=90$.