NIMCET 2017 — Mathematics PYQ

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Question

NIMCET 2017 — Mathematics PYQ

NIMCET | Mathematics | 2017

Let A and B two sets containing four and two elements respectively, The number of subsets of the set $A× B$ , each having at least three elements is:

Choose the correct answer:

Explanation

Concept:
Selection r things out of n things is denoted by $^{n} C_{r}$

$n C_{r} = \frac{n !}{( n - r )! r !}$

Calculation:
Set A has 4 elements
Set B has 2 elements

Total number of elements in $(A \times B) = 4 \times 2 = 8$

Total number of subsets of $(A \times B) = 2^{8} = 256$

Number of subsets having 0 element $=^{8} C_{0} = 1$

Number of subsets having 1 element $=^{8} C_{1} = 8$

Number of subsets having 2 elements $=^{8} C_{2} = \frac{8 \times 7}{2} = 28$

Number of subsets having at least 3 elements
$= 256 - 28 - 8 - 1 = 219$

Hence, option (3) is correct.