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Consider a universe S of n(S) = 8 distinguishable elements.?

. Consider a universe S of n(S) = 8 distinguishable elements.

a. How many subsets of size 1 can be distinguished?

b. How many subsets of size 2 can be distinguished?

c. How many subsets of size 3 can be distinguished?

d. How many subsets of size 4 can be distinguished?

e. How many total subsets of all sizes (NOT counting the empty set and the set S itself) can be distinguished?

1 Answer

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  • 7 years ago
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    Lets label them as A B C D E F G H.

    Below the number of Combinations formula is used : XcY = X! / [(X-Y)! Y!]

    a. n(1) = 8

    {A B C D E F G H}

    b. n(2) = 8c2+8 = 8!/(6! 2!)+8 = (8X7/2)+8 = 28+8 = 36

    {AA AB AC AD AE AF AG AH BB BC BD BE BF BG BH....}

    c. n(3) = 8c3+8²+8 = 8!/(5! 3!)+8²+8 = (8X7X6/3X2)+8²+8 = 56+64+8 = 128

    {AAA AAB AAC AAD AAE AAF AAG AAH BBA BBB BBC BBD BBE BBF BBG BBH....}

    d. n(4) = 8c4+8 = 8!/(4! 4!)+8²+8 = (8X7X6X5/(4X3X2)+8 = 70+8³+8²+8 = 70+512+64+8 = 654

    {AAAA AAAB AAAC AAAD AAAE AAAF AAAG AAAH AABA AABB AABC AABD AABE AABF AABG AABH ....}

    e = a+b+c+d = 8+36+128+654 = 826

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