Respuesta :
Answer:
[tex]1715[/tex]
Step-by-step explanation:
GIVEN: A bibliophile plans to put a total of seven books on her marble shelf. She can choose these seven books from a mixture of works from Antiquity and works on Post-modernism, of which there are seven each.
TO FIND: If the shelf must contain at least four works from Antiquity, and one on Post-Modernism, then how many ways can he select seven books to go on the shelf.
SOLUTION:
Total number of books available [tex]=14[/tex]
As there must be at least [tex]4[/tex] books on Antiquity and [tex]1[/tex] on Post-modernism
Therefore,
when there are [tex]6[/tex] Antiquity books and [tex]1[/tex] on Post-modernism.
total ways of selection [tex]=^7C_6\times^7C_1=49[/tex]
when there are [tex]5[/tex] Antiquity books and [tex]2[/tex] on Post-modernism.
total ways of selection [tex]=^7C_5\times^7C_2=21\times21[/tex]
[tex]=441[/tex]
when there are [tex]4[/tex] Antiquity books on [tex]3[/tex] books on Post-modernism.
total ways of selection [tex]=^7C4\times^7C3=35\times35[/tex]
[tex]=1225[/tex]
Total ways of selection are [tex]=1225+441+49[/tex]
[tex]=1715[/tex]
Hence the total ways of selection such that there are at least [tex]4[/tex] books on Antiquity and [tex]1[/tex] on Post-modernism.
