S= 1,2,3, ldots 20 is to be partitioned into four sets A, B, C and D of equal size. The number of ways it can be done, is

Question

S= 1,2,3, ldots 20 is to be partitioned into four sets A, B, C and D of equal size. The number of ways it can be done, is (A) (20 !/4 ! × 5 !) (B) (20 !/45) (C) (20 !/(5 !)4) (D) (20 !/(4 !)5)

Tardigrade Admin · Accepted Answer

Set S= 1,2,3, ldots, 20 is to be partitioned into four sets of equal size i.e., having 5-5 numbers. The number of ways in which it can be done = 20 C5 × 15 C5 × 10 C5 × 5 C5 =(20 !/15 ! × 5 !) × (15 !/10 ! × 5 !) × (10 !/5 ! × 5 !) × 1 =((20 !)/(5 !)4)

Q. $S = {1, 2, 3, \dots 20}$ is to be partitioned into four sets $A, B, C$ and $D$ of equal size. The number of ways it can be done, is

$\frac{20 !}{4 ! \times 5 !}$

$\frac{20 !}{4 ^{5}}$

$\frac{20 !}{( 5 ! ) ^{4}}$

$\frac{20 !}{( 4 ! ) ^{5}}$

Q. S={1,2,3,…20} is to be partitioned into four sets A,B,C and D of equal size. The number of ways it can be done, is

4!×5!20!​

4520!​

(5!)420!​

(4!)520!​

Set S={1,2,3,…,20} is to be partitioned into four sets of equal size i.e., having 5−5 numbers. The number of ways in which it can be done =20C5​×15C5​×10C5​×5C5​ =15!×5!20!​×10!×5!15!​×5!×5!10!​×1 =(5!)4(20!)​

Q. $S = {1, 2, 3, \dots 20}$ is to be partitioned into four sets $A, B, C$ and $D$ of equal size. The number of ways it can be done, is

$\frac{20 !}{4 ! \times 5 !}$

$\frac{20 !}{4 ^{5}}$

$\frac{20 !}{( 5 ! ) ^{4}}$

$\frac{20 !}{( 4 ! ) ^{5}}$