isi-entrance 2012 Q21

isi-entrance · India · solved Permutations & Arrangements Linear Arrangement with Constraints
In how many ways can $10$ A's and $6$ B's be arranged in a row such that no two B's are adjacent and no two A's are adjacent? (More precisely: find the number of arrangements of $10$ A's and $6$ B's such that between any two consecutive B's there is at least one A, and between any two consecutive A's there is at least one B.)
Total number of ways $= 2 \times {}^9C_3 \times {}^7C_3$. (A) 
In how many ways can $10$ A's and $6$ B's be arranged in a row such that no two B's are adjacent and no two A's are adjacent? (More precisely: find the number of arrangements of $10$ A's and $6$ B's such that between any two consecutive B's there is at least one A, and between any two consecutive A's there is at least one B.)
Paper Questions
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