The set S = {1, 2, 3, . . . , 12} is to be partitioned into three sets A, B and C of equal size. Thus,A∪B∪C=S,A∩B=B∩C=A∩C=ϕThe number of ways to partition S is

A
$12! / 3! (4!)^{3}$
B
$12! / 3! (3!)^{4}$
C
$12! / (4!)^{3}$
D
$12! / (3!)^{4}$

Solution:

.Required number of ways

$\begin{matrix} =^{12} C_{4} \times^{8} C_{4} \times^{4} C_{4} \\ = \frac{12!}{8! 4!} \times \frac{8!}{4! 4!} \times 1 = \frac{12!}{(4!)^{3}} \end{matrix}$

The set S = {1, 2, 3, . . . , 12} is to be partitioned into three sets A, B and C of equal size. Thus, $A \cup B \cup C = S, A \cap B = B \cap C = A \cap C = ϕ$
The number of ways to partition S is

Solution:

Related content