The set S = left{ {1,2,3, ldots ,12} right} i | vedclass

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

Question

are $12$ elements.

Three disjoint sets $A, B$ and $C$ of same size are to be formed.

$\Rightarrow$ Each set has $4$ elements each.

No. of way

Vedclass · Accepted Answer

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

Vedclass · Answer

are $12$ elements.

Three disjoint sets $A, B$ and $C$ of same size are to be formed.

$\Rightarrow$ Each set has $4$ elements each.

No. of ways of selecting any $4$ elements from $12$ elements for set $A=^{12} C_{4}$

No. of ways of selecting any $4$ elements from $8$ elements for set $B=^{8} C_{4}$

No. of ways of selecting any $4$ elements from $4$ elements for set $C=^{4} C_{4}$

Total no. of partitions $=^{12} C_{4} 	imes^{8} C_{4} 	imes^{4} C_{4}$

$=\frac{12 !}{8 ! 4 !} 	imes \frac{8 !}{4 ! 4 !} 	imes \frac{4 !}{0 ! 4 !}=\frac{12 !}{(4 !)^{3}}$

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

Similar Questions

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples, is

In an election there are $8$ candidates, out of which $5$ are to be choosen. If a voter may vote for any number of candidates but not greater than the number to be choosen, then in how many ways can a voter vote

Find the number of ways of selecting $9$ balls from $6$ red balls, $5$ white balls and $5$ blue balls if each selection consists of $3$ balls of each colour.

The number of words (with or without meaning) that can be formed from all the letters of the word $"LETTER"$ in which vowels never come together is

An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then the number of ways in which $4$ marbles can be drawn so that at the most three of them are red is