Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A x B each having at least 3 and at most 6 elements is [2023]

Question

Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A x B each having at least 3 and at most 6 elements is [2023]

Smart Achievers · Accepted Answer

(2)

$Given, n (A) = 5, n (B) = 2$

$∴$ $n (A \times B) = 10$

$∴$ $Required number of subsets =^{10} C_{3} +^{10} C_{4} +^{10} C_{5} +^{10} C_{6}$

$= 120 + 210 + 252 + 210$ $= 792$

Solution

Q.
Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A x B each having at least 3 and at most 6 elements is [2023]

1 752

2 792

3 772

4 782

Ans.
(2)

$Given, n (A) = 5, n (B) = 2$

$∴$ $n (A \times B) = 10$

$∴$ $Required number of subsets =^{10} C_{3} +^{10} C_{4} +^{10} C_{5} +^{10} C_{6}$

$= 120 + 210 + 252 + 210$ $= 792$

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