The number of ways in which 12 books can be put in three shelves with four on each shelf is a. `(12 !)/((4!)^3)` b. `(12 !)/((3!)(4!)^3)` c. `(12 !)/((3!)^3 4!)` d. none of these

The number of ways in which 12 books can be put in 3 shelves, 4 on each is

There are three copies each of four different books. The number of ways in which they can be arranged in a shelf is. a. (12 !)/((3!)^4) b. (12 !)/((4!)^3) c. (21 !)/((3!)^4 4!) d. (12 !)/((4!)^3 3!)

The number of ways in which 12 different objects can be divided into three groups each containing 4 objects is (i) ((12!))/((4!)^(3)(!3)) (ii) ((12!))/((4!)^(3)) (iii) ((12!))/((4!)) (iv) none

A library has a copies of one book, b copies each of two books, c copies each of three books, a single copy of d books. The total number of ways in which these books can be arranged in a shelf is equal to a. ((a+2b+3c+d)!)/(a !(b !)^2(c !)^3) b. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^3) c. ((a+b+3c+d)!)/((c !)^3) d. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^)

A library has a copies of one book, b copies each of two books, c copies each of three books, a single copy of d books. The total number of ways in which these books can be arranged in a shelf is equal to a. ((a+2b+3c+d)!)/(a !(b !)^2(c !)^3) b. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^3) c. ((a+b+3c+d)!)/((c !)^3) d. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^)

A library has a copies of one book, b copies each of two books, c copies each of three books, a single copy of d books. The total number of ways in which these books can be arranged in a shelf is equal to a. ((a+2b+3c+d)!)/(a !(b !)^2(c !)^3) b. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^3) c. ((a+b+3c+d)!)/((c !)^3) d. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^)

A library has a copies of one book, b copies each of two books, c copies each of three books, a single copy of d books. The total number of ways in which these books can be arranged in a shelf is equal to a. ((a+2b+3c+d)!)/(a !(b !)^2(c !)^3) b. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^3) c. ((a+b+3c+d)!)/((c !)^3) d. ((a+2b+3c+d)!)/(a !(2b !)^(c !)^)

There are three copies each of four different books.The number of ways in which they can be arranged in a shelf is.a.(12!)/((3!)^(4)) b.(12!)/((4!)^(3)) c.(21!)/((3!)^(4)4!) d.(12!)/((4!)^(3)3!)

The number of ways that 12 prizes can be divided among 4 students so that each may have 3 prizes is