Answer:
32767 distinct color grouping
Step-by-step explanation:
Given data:
Total tube is 13
for distinct color, group can be 1,2,3,4,.... 15
For total number of ways we have following relation
[tex]^nC_0 +^nC_1 +^nC_2 + .......^nC_n = 2^n[/tex]
here n = 13 so we have
[tex]^15C_0 +^15C_1 +^15C_2 + .......^15C_{15} = 2^15[/tex]
for at least one
[tex]= 2^{15} - 1[/tex]
[tex]= 32768 -1[/tex]
= 32767 distinct color grouping
