Question

In how many ways can a class of 20 students be divided into 3 sets so that three students are int he first set, 5 are in the second, and 12 are in the 3rd?

Answer 1

The total number of ways to divide the class into sets of sizes 3, 5, and 12 is 7,050,720.

To determine the number of ways to divide a class of 20 students into three sets with specified sizes (3, 5, and 12), you can use combinations.

First, choose 3 students out of 20 for the first set:

( 20/3 ) ways to choose 3 students from 20.

Next, choose 5 students out of the remaining 17 for the second set:

( 17/5 ) ways to choose 5 students from the remaining 17.

The rest of the students (20 - 3 - 5 = 12) will automatically form the third set.

Now, you can calculate the total number of ways by multiplying these combinations:

(20/3 )×( 17/5​ )

Let's calculate it:

( 20/3)= 20×19×18/ 3×2×1 =1140

( 17/5 )= 17×16×15×14×13/ 5×4×3×2×1 =6188

Therefore, the total number of ways to divide the class into sets of sizes 3, 5, and 12 is 1140×6188=7,050,720.