Selections and combinations · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Factorials, arrangements and selections — objective 1

Maths4U Original · Short practice

There are \(\displaystyle n=8\) distinct labels and \(\displaystyle r=4\) selected positions or places, as specified in each part. No label can be repeated.

How many ordered selections of r distinct labels are possible?

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Factorials, arrangements and selections — objective 1

Maths4U Original · Short practice

There are \(\displaystyle n=9\) distinct labels and \(\displaystyle r=2\) selected positions or places, as specified in each part. No label can be repeated.

How many ordered selections of r distinct labels are possible?

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Factorials, arrangements and selections — objective 2

Maths4U Original · Short practice

There are \(\displaystyle n=9\) distinct labels and \(\displaystyle r=2\) selected positions or places, as specified in each part. No label can be repeated.

How many unordered r-label subsets are possible?

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Factorials, arrangements and selections — objective 2

Maths4U Original · Short practice

There are \(\displaystyle n=10\) distinct labels and \(\displaystyle r=3\) selected positions or places, as specified in each part. No label can be repeated.

How many unordered r-label subsets are possible?

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Factorials, arrangements and selections — objective 3

Maths4U Original · Short practice

There are \(\displaystyle n=10\) distinct labels and \(\displaystyle r=3\) selected positions or places, as specified in each part. No label can be repeated.

How many complete orders keep two specified labels adjacent?

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Factorials, arrangements and selections — objective 3

Maths4U Original · Short practice

There are \(\displaystyle n=6\) distinct labels and \(\displaystyle r=4\) selected positions or places, as specified in each part. No label can be repeated.

How many complete orders keep two specified labels adjacent?

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Factorials, arrangements and selections — objective 4

Maths4U Original · Short practice

There are \(\displaystyle n=6\) distinct labels and \(\displaystyle r=4\) selected positions or places, as specified in each part. No label can be repeated.

How many r-label subsets contain one specified label?

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Factorials, arrangements and selections — objective 4

Maths4U Original · Short practice

There are \(\displaystyle n=7\) distinct labels and \(\displaystyle r=2\) selected positions or places, as specified in each part. No label can be repeated.

How many r-label subsets contain one specified label?

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →