Question

- If a set A has 6 elements, then the number of subsets
of A containing atleast 3 elements is
(a) 63 (b) 57 (c) 42 (d) 40
Cod
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Answer 1

Answer:

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Answer 2

Answer:

Option c. 42

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Step-by-step explanation:

Set A has : 6 elements

sub set atleast 3 elements

Total element: 2^n

= 2⁶

=64

formula:

nCr = n! /r! (n – r)!

C = Number of combination

n = Total number of objects in a set

r = r is the number of choosing objects fron set

! = factorial

3elements = Total element - ( 0 element - 1 element - 2 element)

wel,

6C0 = 6! /0!(6-0)! = 6! /0! 6! = 1

6C1 = 6! /1!(6-1)! = 6! /1! 5! = 6×5! /5!×1 = 6

6C2 = 6! /2!(6-2)! = 6! /1! 4! = 6×5×4! /4! × 2 = 15

= 64- ( 1+6+15)

= 64- 22

= 42

Answer is 42

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