Question

Kelly has different books to arrange on a shelf; 2 blue, 4 green, and 3 red. Answer parts a through e below. (a) In how many ways can the books be arranged on a shelf? way(s) (Type a whole number.) (b) If books of the same color are to be grouped together, how many arrangements are possible? way(s) (Type a whole number.) (c) In how many distinguishable ways can the books be arranged if books of the same color are identical but need not be grouped together. way(s) (Type a whole number.) (d) In how many ways can you select 3 books, one of each color, if the order in which the books are selected does not matter. way(s) (Type a whole number.) (e) In how many ways can you select 3 books, one of each color, if the order in which the books are selected matters. way(s) (Type a whole number.)

Answer 1

If you have any doubts in the solution please ask me in comments here i use basic idea of permutation and combination...

** Solution given that helly has diffrent books to arrange on a Shelf ; 2 Blue, 4 green, 3 red j total Balls kelly have 4+2+ 3 = 9 9. ca) Soletion: NOCO to determine that How many way can the Books be arranged on the self there are total 9- Books NO of way that on a shelf - 9! Books can be arranged 362,880 Answer (6) soicehon If the Books of the same color are to be 9-сосеред we have these type of arranged together then R R R B B G G total group = 3 1 1 1 So NOOD 3! way group can be arranged Books can be arranged 4! 2! 3) inside each group Νοιω No. of ways that same color are to be grouped together = 31 4! 2! 3! 1728 Answer- Soluton ways are that Books can No. of ways be arranged when duistinguashable = 9! 1260 4! 3! 2! No. of disting washable ways thet Books can be arranged 1260 Answer

46, 30, .22.31 if we 46, 2010 (d) Select three Book, one of each colou, R the onder of selection doesn't matter then way to one book form green, Blue, red arre respectively. Select choosen one of each No. of ways that selection of Selection of 3 - Books Colom 46, 20, 30, 4 X 3 X2 24. 24 Answer. (e) Soive! NOW to determine the No. of ways that to select 3 - Books one - of each colour ; & the order of seclection matter onre . Blue , green to select NO: Op way Book from respectively. red are 4G , 20, 3c, the selection Buste Now the order the order of selection metters SO can be done 3! ways ways 3 - Books , colo No. of to select one of each } is selection matter Coreler) = when 144 Answer