Carcass wrote:
A chemist is testing 6 different liquids. For each test, the chemist chooses 2 of the liquids and mixes them together. What is the least number of tests that must be done so that every possible combination of liquids is tested?
Question is pick 2 (r) from a set of 6 (n) without replacing and order does not matter. Formula is \(nC_r = 6C_2 = \frac{(6*5)}{2} =15\)
Solving without formula:
Let chemicals be A,B,C,D,E,F and the possible options are
i) with A , there are 5 options (AB, AC, AD, AE and AF)
ii) with B, there are 4 options, (BC, BD, BE and BF),
iii) with C, there are 3 options, (CD, DE and CF)
iv) with D, there are 2 options, (DE and DF)
v) with E, there is 1 option (EF)
So 1+2+3+4+5 = 15