in how many ways can 11 books on english and 9 books on french be placed in a row on a shelf so that two books on french may not be together ?
we have 11 english and 9 french books , no french books should be adjacent . imagine 11 english books in a row and empty slots like below : * e * e * e * e * e * e * e * e * e * e * e * now if 9 french books would be placed in 12 empty slots , all french books will be separated by english books . so we can ` ` choose ' ' 9 empty slots from 12 available for french books , which is 12 c 9 = 220 . ans : a _________________
add(add(choose(subtract(11, const_1), const_3), permutation(subtract(11, const_1), const_2)), choose(subtract(11, const_1), const_1))