Permutation and CombinationHard
Question
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 number 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 :
Options
A.nP2. mPm. (n - 2) !
B.mP2. nPn. (n - 2) !
C.nP2. nPn. (m - 2) !
D.none
Solution
For P → If same species are different
Total number of arragements is nP2 . (m + n - 2) !
For Q → If same species are alike then number of arrangement is
Hence
= nP2 . m! . (n - 2)! = nP2 . mPm . (n - 2)!
Total number of arragements is nP2 . (m + n - 2) !
For Q → If same species are alike then number of arrangement is
Hence
= nP2 . m! . (n - 2)! = nP2 . mPm . (n - 2)! Create a free account to view solution
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