Home
Class 12
MATHS
The number of ways of partitioning the s...

The number of ways of partitioning the set `{a,b,c,d}` into one or more non empty subsets is

A

`14`

B

`15`

C

`16`

D

`17`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `{:("Partitioning",,"Number of ways"),(4"members",,1),(1+3"members",,(4!)/(1!3!)=4),(2+2"members",,(4!)/((2!)^(2)2!)=3),(1+1+2"members",,(4!)/((1!)^(2)2!2!)=6),(1+1+1+1"members",,(4!)/((1!)^(4)4!)=1),("Total",,15"ways"):}`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|2 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Matching Column Type|1 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE PUBLICATION|Exercise Sovled Examples|22 Videos

Similar Questions

Explore conceptually related problems

The number of subsets of a set containing n distinct elements is

A is a set containing n different elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P . A subset Q of A is again chosen. The number of ways of choosing P and Q so that PnnQ contains exactly two elements is a. .^n C_3xx2^n b. .^n C_2xx3^(n-2) c. 3^(n-1) d. none of these

Set A={a,b,c,d} then the number of defined relation in A is

A,B,C,D develop 18 items. Five items jointly by A and C , four items by A and D , four items by B and C and five items by B and D . The number of ways of selecting eight ites out of 18 so that the selected ones belong equally to A,B,C,D is

In how any different ways can a set A of 3n elements be partitioned into 3 subsets of equal number of elements? The subsets P ,Q ,R form a partition if PuuQuuR=A ,PnnR=varphi,QnnR=varphi,RnnP=varphidot

Two finite sets A and B are having m and n elements.The total number of subsets of the first set is 56 more than the total number of subsets of the second set.The value of m and n ae respectively.

Two finite sets have ma nd n elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then the values of m and n respectively are-

Define a binary opeartion ** on a non-empty set A.

Define an associative binary operation on a non-empty set S.

Write down all the subsets of the set : {a, b}