Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
Let Set A = {1,2,3,4} & Set B = { a,b}
=> A x B contains 4*2 = 8 elements ( or ordered pairs),
Like A x B = { (1,a),(1,b),(2,a),(2,b),(3,a),(3,b),(4,a)(4,b) }
So, A x B contains 8 ordered pairs.
Now we need to find the subsets of A x B , in which at least 3 elements ie 3 ordered pairs should be there. That means it can have 8 ordered pairs or 7 ordered pairs or 6pairs or 5pairs or 4pairs or 3 pairs. It can not go below 3 pairs as question is we need subsets with at least 3 pairs.
So we start making the subsets with 8 pairs.
●With 8 ordered pairs…. we have just 1 subset , which is {(1,a),(1,b),(2,a,),(2,b),(3,a),(3,b),(4,a),(4,b)} (as such , every set is its own subset)
●similarly with 7 ordered pairs : the number of ways of choosing 7 pairs from the set of 8 pairs will be= 8C7 = 8!/(1! * 7!) = 8 subsets
● Now similarly with 6 pairs : we get 8C6
= 8!/(2! * 6!) = 28 subsets
● With 5 pairs : we get 8C5 = 8!/(3!*5!) = 56 subsets
● With 4 pairs : we get 8C4 = 8!/(4!*4!) = 70 subsets
●Now with 3 pairs: we get 8C3 = 8!/(5!*3!) = 56 subsets
Now, by adding all the above subsets , we get..
1 + 8 + 28 + 56 + 70 + 56 = 219 subsets . . . . Ans
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !