The set S = {1, 2, 3, dots, 12} is partitione | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The set $S$ contains $12$ elements. Since it is partitioned into three sets $A, B, C$ of equal size,each set must contain $12 / 3 = 4$ elements.Th

Vedclass · Accepted Answer

$\frac{12!}{(4!)^3}$

Vedclass · Answer

(B) The set $S$ contains $12$ elements. Since it is partitioned into three sets $A, B, C$ of equal size,each set must contain $12 / 3 = 4$ elements.The number of ways to choose $4$ elements for set $A$ is $\binom{12}{4}$.The number of ways to choose $4$ elements for set $B$ from the remaining $8$ is $\binom{8}{4}$.The number of ways to choose $4$ elements for set $C$ from the remaining $4$ is $\binom{4}{4}$.Since the sets $A, B, C$ are distinct (labeled),the total number of ways is:$\binom{12}{4} 	imes \binom{8}{4} 	imes \binom{4}{4} = \frac{12!}{4! 	imes 8!} 	imes \frac{8!}{4! 	imes 4!} 	imes \frac{4!}{4! 	imes 0!} = \frac{12!}{(4!)^3}$.

The set $S = \{1, 2, 3, \dots, 12\}$ is partitioned into three sets $A, B, C$ of equal size such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = C \cap A = \phi$. In how many ways can $S$ be partitioned?

Similar Questions

The number of ways of dividing $52$ cards amongst four players equally is

Consider a square matrix of order $5$ such that $a_{ij} = 0$ for all $i + j = 6$,where $a_{ij} \in \{0, 1\}$ for all $i, j$. In each row as well as in each column,there is only one non-zero element. Then,the number of such matrices is:

Three letters,to each of which corresponds an envelope,are placed in the envelopes at random. The probability that all the letters are not placed in the right envelopes is

In an examination,$5$ students have been allotted their seats as per their roll numbers. The number of ways,in which none of the students sits on the allotted seat,is $..........$.

In how many ways can $52$ cards be distributed equally among four players?

Vedclass Test Series

Exam Paper Generator

Online Exam Module