determine the number of distinct proper subsets of 1,2,3,8

Question

determine the number of distinct proper subsets of 1,2,3,8

Answer 1

{1,2,3,8} is a subset but not a proper subset

16-1 = 15 proper subsets

16 subsets

proper subsets of a set with n elements is 2^n -1

if n=4

2^4 - 1 = 16-1 = 15

{1,2,3}

{1,2,8}

{1,3,8}

{2,3,8}

{1,2}

{1,3}

{1,8}

{2,3}

{2,8}

{3,8}

{1}

{3}

{8}

{2}

null set {}

nCr = n!/r!(n-r)

4C0 = 4!!/0!4!= 1

4C1 = 4!/1!3!= 4

4C2 = 4!2!2!=6

4C3 = 4!/3!1! = 4

4C4 = 4!/4!0! = 1

4C0 + 4C1 + 4C2 +4C3 + 4C4 =

1+4+6+4+1 =16

Pascal's Triangle

1

11

121'

1331

14641

1+4+6+4+1 = 16

coefficients of terms in 4th degree polynomial

(a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4

1,4,6,4,1

a proper subset of A is B where there is at least one element of A that is not in B

if A = {1,2,3,8} then there are 16 subsets but only 15 proper subsets