Question

Calcula: a) CR7,5 b) CR5,7 c) CR10,6 d) CR6,10

Answer 1

Las combinaciones con repetición de m elementos tomados de n en n, con m ≥n se calculan mediante la expresión

                                   $\displaystyle\ CR(m,n) = \left(\begin{array}{c}m+n-1\\n\\\end{array}\right)$

Luego

$\displaystyle\ CR(7,5) = \left(\begin{array}{c}7+5-1\\ 5\\\end{array}\right) = \left(\begin{array}{c}11\\ 5\\\end{array}\right) = \frac{11!}{5!6!} = 462$

$\displaystyle\ CR(5,7) = \left(\begin{array}{c}7+5-1\\ 7\\\end{array}\right) = \left(\begin{array}{c}11\\ 7\\\end{array}\right) = \frac{11!}{4!7!} = 330$

$\displaystyle\ CR(10,6) = \left(\begin{array}{c}10+6-1\\ 6\\\end{array}\right) = \left(\begin{array}{c}15\\ 6\\\end{array}\right) = \frac{15!}{5!10!} = 5005$

$\displaystyle\ CR(6,10) = \left(\begin{array}{c}10+6-1\\ 10\\\end{array}\right) = \left(\begin{array}{c}15\\ 10\\\end{array}\right) = \frac{15!}{5!10!} = 3003$