MediumMathematics
+4 / -1
The set S = {1,2,3, ...,15} is to be partitioned into three sets A, B, C of equal size. Thus A ∪ B ∪ C = S, A ∩ B = B ∩ C = A ∩ C = ϕ. What is the number of ways to partition S?
A
15!/(5!)^3
B
15!/(5!)^4
C
15!/(3!(5!)^3
D
15!/(3!(5!)^5
Explanation
As A, B and C are mutually exclusive and exhaustive sets, each of them will have equal and unique elements. i.e., A will have 5 different and unique elements (5 numbers will be selected out of 15), B will also have 5 different and unique elements (5 numbers will be selected out of remaining 10) as well as C will also have 5 different and unique elements (5 numbers will be selected out of remaining 5). ⇒ No. of ways of partition of S is = 15C5 × 10C5 × 5C5 = 15!/(5!10!) × 10!/(5!5!) × 5!/(5!0!) = 15!/(5!)^3.
Previous
If n(A) = 5, n(B) = 10 and n(C) = 20 for three disjoint sets A, B and C, then wh
NextIf A = {0,ϕ,{8}}, what will be the number of subsets of P(A)?
More from Sets
Hard
Let A₁, A₂, A₃, ..., A₁₀₀ be 100 sets such that n(Aᵢ) = i + 1 and A₁ ⊂ A₂ ⊂ A₃ ⊂ ⋯ A₁₀₀, then ⋃ᵢ₌₁⁶⁰
HardIf A₁ ⊂ A₂ ⊂ A₃ ⊂ ⋯ ⊂ A₅₀, and n(Aᵢ) = i – 1, then n(⋂ᵢ₌₁₁⁵⁰ Aᵢ) is equal to:
HardIf A = {(x, y): x² + y² ≤ 1, x,y ∈ R} and B = {(x, y): x² + y² ≤ 4, x,y ∈ R}, then
MediumTwo finite sets have m and n elements respectively. The total number of subsets of first set is 56 m
MediumWhich option is representing the given Venn diagram?
EasyIf A and B are two sets, then (A – B)∩(B – A)∩(A ∩ B) equals to:
Practice Mathematics Exams
Full-length mock tests with detailed analytics, rank, and percentile.
Browse Exams