JEE-Mains 2015 (1/30)

Let A A and B B are two sets containing four and two elements respectively. Then the number of subsets of the set A × B A \times B , each having at least three elements is:

510 219 256 275

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2 solutions

Satvik Choudhary
Jun 13, 2015

The no. Of ordered pairs in the set A×B is 4 × 2 = 8 4×2=8 So no of total subsets of A×B is 2 8 = 256 2^{8}=256

We have to subtract the subsets which have less than 3 elements from the total no. Of subsets 256 8 C 0 8 C 1 8 C 2 = 256 1 8 28 = 219 256-^{8}C_{0}-^{8}C_{1}-^{8}C_{2}=256-1-8-28=219

The options are too lame, only one of them fits!! LOL... Never thought that IIT paper setters would make such gaffes.

Krishna Ar - 6 years ago

A better option for binomial coefficients is to use ( n r ) \dbinom{n}{r} instead of n C r ^n\mathrm{C}_r since the latter is not known to many and is not commonly used. The former is the commonly used notation.

Prasun Biswas - 6 years ago
Vishnu Bhagyanath
Jun 14, 2015

Number of subsets = 2 m n 2^{mn} = 2 8 2^8 = 256 256 . The answer would be less than that, the only option valid being 219.

i did the same !!!

Rishabh Jain - 5 years, 12 months ago

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