Permutations and Combinations

Evaluate Factorial Expressions

Introduction to Permutations

Continued Permutations

Introduction to Combinations

Continued Combinations

Pascal's triangle

Binomial Expansions and Coefficients

Further Binomial Expansions

Class XI

Mixed problem

Interactive practice questions

If you can choose one item from a group of $a$a items and a second item from a group of $b$b items, what is the total number of two-item choices?

Easy

1min

The number of possible permutations of $r$r objects taken from $n$n items is $\nPr{n}{r}$nPr. Express this in factorial form.

Easy

1min

The number of possible combinations of $r$r objects taken from $n$n items is $\nCr{n}{r}$nCr. Express this in factorial form.

Easy

< 1min

Evaluate $\frac{\nPr{8}{3}}{3!}-\nCr{8}{3}$8P33!−8C3.

Easy

1min

Outcomes

11.A.PC.1

Fundamental principle of counting. Factorial n. Permutations and combinations, derivation of formulae and their connections, simple applications.

11.A.BT.1

Statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications.

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