Question

let be a set with 11, let be a set with 10, and let be a set with 3. for any function , how many different restrictions of to are there?

Answer 1

The total number of different restrictions of a function from a set with 11 elements to a set with 3 elements is 990.

Step-by-step explanation:

The question seems to be about finding the numbe of restrictions of a function from a set with 11 elements (let us call it set A) to a set with 3 elements (let us call it set B).

To calculate this, we observe that a restriction of f to set B involves selecting which 3 elements of set A are to be mapped into set B. For each of those selections, there are 3! ways to arrange the elements of set A into set B, since each element in set B has to be mapped to a unique element in set A.

Therefore, the calculation will be the number of ways to choose 3 elements out of 11, multiplied by the number of ways to arrange those 3 elements. The number of ways to choose 3 elements from 11 is C(11, 3), which is 165, and for each of these selections, there are 3! = 6 ways to arrange them.

Thus, the total number of different restrictions is 165 * 6 = 990.