To furnish a room one has to select 2 chairs and 2 tables from a collection of chairs and tables that are different from each other. If there are 5 chairs in the collection and there are 150 different combinations available, how many tables are there??
2007-02-06 17:46:13 · 3 answers · asked by rajagopal r 1 in Science & Mathematics ➔ Mathematics
There are 5C2 = 5*4/2 = 10 ways to choose 2 chairs.
Since there are 150 total different combinations, there are 150/10 = 15 ways to choose the 2 tables.
xC2 = x*(x-1)/2 = 15, and by quick guess and check, you can see that x - the number of tables - has to be 6.
2007-02-06 17:51:56 · answer #1 · answered by Q 2 · 0⤊ 0⤋
The number of combinations in the sense of this problem = (the number of combinations of chairs) * (the number of combinations of tables).
Pause for a moment to realize why.
The number of combinations of chairs is (5 x 4)/(2 x 1), aka "5 choose 2".
That turns out to be 10.
So the number combinations of tables has to be 15.
So find the T such that "T choose 2" = 15.
2007-02-07 01:51:50 · answer #2 · answered by Curt Monash 7 · 0⤊ 0⤋
a lot
wow, that is my first dumb answer
2007-02-07 02:00:19 · answer #3 · answered by jennainhiding 4 · 0⤊ 0⤋