Question 1025984
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if a given set has nine elements, how many of its subsets have at least five elements?
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<pre>
{{{C[9]^0 + C[9]^1 + C[9]^2 + C[9]^3 + C[9]^4 + C[9]^5}}} = 

= 1 + 9 + 36 + 84 + 126 + 126 = 382,

where {{{C[n]^k}}} is the number of combinations of n things taken k at a time.

There is {{{C[9]^0}}} = 1 empty subset.

There are {{{C[9]^1}}} = 9 subsets consisting of 1 element.

There are {{{C[9]^2}}} = 36 subsets consisting of 2 elements.

There are {{{C[9]^3}}} = 84 subsets consisting of 3 elements.

There are {{{C[9]^4}}} = 126 subsets consisting of 4 elements.

There are {{{C[9]^5}}} = 126 subsets consisting of 5 elements.

Regarding combinations, see the lesson <A HREF=https://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A> in this site.


</U>Answer</U>. 382 subsets, including one empty subset.
</pre>

<U>Notice</U>.


Dear Mr. Edwin McCravy,


in your post you publicly said that my solution is incorrect.


But is IS correct due to obvious reasons.


So I ask you to make a public acknowledgment in your post,
that you take your words back and recognize that you were wrong and my solution is correct.


It doesn't require much time to get the right conclusion.
Finally, it is important for the student to know the truth.


If it is difficult to you to make such contr-statement,
you can simply change your post correspondingly.


When I see it, I will take off this <U>notice</U> from my post.


Thank you.