grandes-ecoles 2016 QII.B.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 $S(p, 0) = 0$.
Deduce an expression of $S(p, n)$ for $p \geqslant n$.

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 $S(p, 0) = 0$.

Deduce an expression of $S(p, n)$ for $p \geqslant n$.

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