Question 815164: if the number of subsets with 4 elements of a set A is equal to the number of subsets with 5 elements of the set,then the number of subsets with 3 elements of this set is?please tell the answer...
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! All problems in math involve logic, but many tricks invented by geniuses before us are taught in math class, so we do not have to reinvent gunpowder every time.
This problem gets easier with a knowledge of combinatorics.
It can be solved without that by a fifth grader, but not easily.
COMBINATORICS:
If combinations of N elements taking 4 at a time equals combinations of N taken 5 at a time, then
N=4+5=9.
Then, combinations of 9 taking 3 at a time is
9*8*7 / (3*2) = 
FIFTH GRADE LOGIC:
If choosing a group of 4 of your friends to go fishing with you is the same as choosing the 5 friends who will not go, you must have
4 + 5 = 9 friends.
The same smart 5th grader will figure out that when making a list of 3 friends to take camping there would be 9 choices for the first name, 8 choices for the second, and 7 choices for the third, for a total of
9*8*7=504 possible lists.
He (or she) would then realize that each set of 3 names appears several times in his 504 lists, because with 3 names there are 3 choices for first and 2 choices for second, for a total of
2*3=6 lists.
So, if each set of 3 friends appears 6 times (listed in different orders) in his 504 lists, the number of sets of 3 friends is
504/6 = 
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