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  4. There are m apples and n oranges to be placed in a line such that the two extreme fruits being both oranges . Let P denotes the numbe of arrangements if the fruits of the same species are different and Q the corresponding figure when the fruits of the same species are alike, then the ratio P / Q has the value equal to :

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Q. There are $m$ apples and $n$ oranges to be placed in a line such that the two extreme fruits being both oranges . Let $P$ denotes the numbe of arrangements if the fruits of the same species are different and $Q$ the corresponding figure when the fruits of the same species are alike, then the ratio $P / Q$ has the value equal to :

Permutations and Combinations

Solution:

$P ={ }^{ n } C _2 \cdot 2 !( m + n -2) ! \quad ; \quad Q =\frac{( m + n -2) !}{( n -2) ! m !}$