Combinations with repetition

Find out how many different ways you can choose k items from n items set. With/without repetition, with/without order.

(n)
(k)

Calculation:

Ck′(n)=(n+k−1k)  n=11 k=3  C3′(11)=C3(11+3−1)=C3(13)=(133)=13!3!(13−3)!=13⋅12⋅113⋅2⋅1=286C'_k(n) = \dbinom{ n+k-1}{ k} \ \\ \ \\ n = 11 \ \\ k = 3 \ \\ \ \\ C'_{ 3 }( 11 ) = C_{ 3 }( 11 + 3 - 1 ) = C_{{ 3}}(13) = \dbinom{ 13}{ 3} = \dfrac{ 13! }{ 3!(13-3)!} = \dfrac{ 13 \cdot 12 \cdot 11 } { 3 \cdot 2 \cdot 1 } = 286

Number of combinations with repetition: 286