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# How many different subsets are there of the set of integers

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Current Student
Joined: 29 Jan 2005
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How many different subsets are there of the set of integers [#permalink]  19 Aug 2006, 22:42
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How many different subsets are there of the set of integers 1-10, exclusive, that contain an odd number of elements?
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

Kudos [?]: 121 [0], given: 0

512

When 1 element selected = 10
When 3 elements selected = 10C3 = 120
When 5 elements selected = 10C5 = 252
When 7 elements selected = 10C7 = 120
When 9 elements selected = 10C9 = 10

Total = 512
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Current Student
Joined: 29 Jan 2005
Posts: 5244
Followers: 23

Kudos [?]: 179 [0], given: 0

ps_dahiya wrote:
512

When 1 element selected = 10
When 3 elements selected = 10C3 = 120
When 5 elements selected = 10C5 = 252
When 7 elements selected = 10C7 = 120
When 9 elements selected = 10C9 = 10

Total = 512

CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

Kudos [?]: 121 [0], given: 0

GMATT73 wrote:
ps_dahiya wrote:
512

When 1 element selected = 10
When 3 elements selected = 10C3 = 120
When 5 elements selected = 10C5 = 252
When 7 elements selected = 10C7 = 120
When 9 elements selected = 10C9 = 10

Total = 512

So this should be

When 1 element selected = 8
When 3 elements selected = 8C3 = 56
When 5 elements selected = 8C5 = 56
When 7 elements selected = 8C7 = 8

Total = 128

I noticed that total numbers of subsets are 2^8 and half of these are with odd number of elements and half with even number of elements.
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Current Student
Joined: 29 Jan 2005
Posts: 5244
Followers: 23

Kudos [?]: 179 [0], given: 0

Good boy. You get a special Japanese wafer cookie sandwich for your effort: ---> http://www.rokkatei.co.jp/top.html
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