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. 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?

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

As there must be at least books on  Antiquity and on Post-modernism

Therefore,

when there are Antiquity books and on Post-modernism.

total ways of selection

when there are Antiquity books and on Post-modernism.

total ways of selection

when there are Antiquity books on books on Post-modernism.

total ways of selection

Total ways of selection are

Hence the total ways of selection such that there are at least books on  Antiquity and on Post-modernism.

don't know what that says sorry i can't you

step-by-step explanation:

idk what it says

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.