Four writers must write a book containing 17 chapters. The first and third writer must write 5 chapters each, the second writer must write 4 chapters and fourth writer must write three chapters. The number of ways that can be found to divide the book between four writers, is

Question

Four writers must write a book containing 17 chapters. The first and third writer must write 5 chapters each, the second writer must write 4 chapters and fourth writer must write three chapters. The number of ways that can be found to divide the book between four writers, is (A) (17!/(5!)2 4! 3! 2!) (B) (17!/5! 4! 3! 2!) (C) (17!/(5!)2 4! 3! ) (D) (17!/(5! )2×4 × 3)

Tardigrade Admin · Accepted Answer

Evidently (c) is correct option because we have to divide 17 into four groups each distinguishable into groups of 5, 5, 4 and 3

Q. Four writers must write a book containing $17$ chapters. The first and third writer must write $5$ chapters each, the second writer must write $4$ chapters and fourth writer must write three chapters. The number of ways that can be found to divide the book between four writers, is

$\frac{17 !}{( 5 ! ) ^{2} 4 ! 3 ! 2 !}$

$\frac{17 !}{5 ! 4 ! 3 ! 2 !}$

$\frac{17 !}{( 5 ! ) ^{2} 4 ! 3 !}$

$\frac{17 !}{( 5 ! ) ^{2} \times 4 \times 3}$

Evidently $(c)$ is correct option because we have to divide $17$ into four groups each distinguishable into groups of $5$ , $5$ , $4$ and $3$

Q. Four writers must write a book containing 17 chapters. The first and third writer must write 5 chapters each, the second writer must write 4 chapters and fourth writer must write three chapters. The number of ways that can be found to divide the book between four writers, is

(5!)24!3!2!17!​

5!4!3!2!17!​

(5!)24!3!17!​

(5!)2×4×317!​