The total number of ways to select 2 students from the 3 clubs is 55 ways.
Since there are three clubs which each has 10, 4 and 5 students, and we require the number of ways a teacher can select 2 students so that they are from different clubs.
Since order doesn't matter and anybody can be chosen first, we use combination theory.
<h3 /><h3>Number of ways of selecting from the first two clubs</h3>
Since we have two slots, to select the first person from the first club, we ¹⁰C₁. For the second student from the club of 4, we have ⁴C₁. Also, there are 2 ways of selecting the two students.
So, there are ¹⁰C₁ × ⁴C₁/2!
= 10 × 4/2
= 20 ways from the first two clubs.
<h3 /><h3>Number of ways of selecting from the next two clubs</h3>
For the next two clubs of 4 and 5 students, for the first slot, we have ⁴C₁. For the second student, we have ⁵C₁. Also, there are 2 ways of selecting the two students.
So, there are ⁴C₁ × ⁵C₁/2!
= 4 × 5/2
= 10 ways from the next two clubs.
<h3 /><h3>Number of ways of selecting from the last two clubs</h3>
For the first and last club of 10 and 5 students, for the first slot, we have ¹⁰C₁. For the second student, we have ⁵C₁. Also, there are 2 ways of selecting the two students.
So, there are ¹⁰P₁ × ⁵P₁/2!
= 10 × 5/2
= 25 ways from the first and last club.
<h3 /><h3>Total number of ways of selecting two students from the 3 clubs.</h3>
So, the total number of ways to select 2 students from the 3 clubs is 20 + 10 + 25 = 55 ways.
So, the total number of ways to select 2 students from the 3 clubs is 55 ways.
Learn more about combinations here:
brainly.com/question/25990169
