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Q4.(a)We denote French by F and Spanish by S and German by G. Thus the details given arelike:2514126nFSGnGSnSnFnFSWe have to find now the nGF=?Thus, it is clear from the statement that each 6 students who speak German (G) speaksany one of the languages from French and Spanish as well.6665 2633nGFSnGFSnGFGSnGFnGSnGFGSnGFnGFnGFHence the answer is 3(b)( ) 6() 6......(1)() 6........(2)nGandeithernGFornGSBut above both are not true at the same time, thus if statement (1) is true then() 0nGSAnd if statement (2) is true then() 0() ( ) ( ) ( ) () () () ()6 12 14 6 0 6 234 1222nGFnGFSnGnFnSnGFnGSnFSnFGSSimilarly if () 0() 6() 22( ) () ()25 22 ()3ccccccnGFnGSthennGFSnUnFGSnGFSnGFSThus, number of people who speaks none of the languages is 3.Q2.(a)As there are 4 red books and 5 black books and total are 9 books so the order in which thebooks are placed with no restrictions is factorial of 9 that is 9!9! = 9 *8*7*6*5*4*3*2*1=362,880The answer is 362,880(b)

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