Question

Suppose you have 13 tubes of paint. How many distinct color groupings can you make with your paint?

Answer 1

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

$^nC_0 +^nC_1 +^nC_2 + .......^nC_n = 2^n$

here n = 13 so we have

$^15C_0 +^15C_1 +^15C_2 + .......^15C_{15} = 2^15$

for at least one

$= 2^{15} - 1$

$= 32768 -1$

= 32767 distinct color grouping