grandes-ecoles 2016 QII.A.3

grandes-ecoles · France · centrale-maths2__pc Combinations & Selection Counting Functions or Mappings with Constraints

For every pair $(p, k)$ of nonzero natural numbers, we denote by $S(p, k)$ the number of surjections from $\llbracket 1, p \rrbracket$ to $\llbracket 1, k \rrbracket$. Consistently, for every $p \in \mathbb{N}^*$, we set $S(p, 0) = 0$.
Determine $S(n+1, n)$.

For every pair $(p, k)$ of nonzero natural numbers, we denote by $S(p, k)$ the number of surjections from $\llbracket 1, p \rrbracket$ to $\llbracket 1, k \rrbracket$. Consistently, for every $p \in \mathbb{N}^*$, we set $S(p, 0) = 0$.

Determine $S(n+1, n)$.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.A.5 QI.A.6 QI.A.7 QI.A.8 QI.A.9 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.B.5 QI.B.6 QI.B.7 QII.A.1 QII.A.2 QII.A.3 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QII.C QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.A.5 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C.1 QIII.C.2 QIII.C.3 QIII.C.4 QIII.C.5 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2 QIV.C.3