To solve this problem, let's break it down step-by-step:
1. Find the number of blue counters:
Given that [tex]\(\frac{3}{5}\)[/tex] of the counters are blue, we calculate the number of blue counters by multiplying the total number of counters by [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
\text{Number of blue counters} = 180 \times \frac{3}{5}
\][/tex]
[tex]\[
180 \times \frac{3}{5} = 108
\][/tex]
So, there are 108 blue counters.
2. Find the number of yellow counters:
Given that [tex]\(\frac{1}{4}\)[/tex] of the counters are yellow, we calculate the number of yellow counters by multiplying the total number of counters by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\text{Number of yellow counters} = 180 \times \frac{1}{4}
\][/tex]
[tex]\[
180 \times \frac{1}{4} = 45
\][/tex]
So, there are 45 yellow counters.
3. Find the number of pink counters:
The total number of counters is the sum of the blue counters, yellow counters, and pink counters. To find the number of pink counters, we subtract the number of blue and yellow counters from the total number of counters.
[tex]\[
\text{Number of pink counters} = \text{Total counters} - \text{Number of blue counters} - \text{Number of yellow counters}
\][/tex]
[tex]\[
\text{Number of pink counters} = 180 - 108 - 45
\][/tex]
[tex]\[
180 - 108 = 72
\][/tex]
[tex]\[
72 - 45 = 27
\][/tex]
So, there are 27 pink counters.
### Summary:
- Number of blue counters: [tex]\( 108 \)[/tex]
- Number of yellow counters: [tex]\( 45 \)[/tex]
- Number of pink counters: [tex]\( 27 \)[/tex]
Therefore, the number of pink counters is [tex]\( \boxed{27} \)[/tex].
