Algebra> Let A&B r two sets contain 4&2 elements r...

Let A&B r two sets contain 4&2 elements respectively then no. Of subset of the setA×B,each having at least three elements

Pritam , 7 Years ago

Grade 12th pass

3 Answers

SHIVANSH MANI

Last Activity: 7 Years ago

Set A has 4 elements

Set B has 2 elements

Number of elements in set (A x B) = 4 x 2 = 8

Total number of subsets of (A x B) = 28 = 256

Number of subsets having 0 elements = 8c0 = 1

Number of subsets having 1 element each = 8c1 = 8

Number of subsets having 2 elements each = 8c2= 8!/(2!6!)=8*7/2=28

Number of subsets having at least 3 elements

= 256 - 1 - 8 - 28 = 256 - 37 = 219

So the answer is 219.

Approved

Rahul Sachdeva

Last Activity: 7 Years ago

No. Of element in A×B =4×2 =8Then no. Of subset of A×B of atleast three element is 8c3+8c4+--------8c8 =8c0+8c1+8c2+8c3+------8c8-8c0-8c1-8c2=2^8-8c0-8c1-8c2=256-1-8-28=219

rohit

Last Activity: 6 Years ago

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