Answer to Question #96233 in Combinatorics | Number Theory for Michael Capobianco

Question

In how many ways could you arrange a display of stationery supplies consisting of 14 notebooks, 5 reams of lined paper, and 50 pens if all the items are laid out in a row?

Answer 1

The number of multiset permutations of M = m1 + m2 + m3 = 50+14+5 is given by the multinomial coefficient

$M!/(m1! *m2!*m3! ) = (50+14+5)! / (50! * 14! *5! ) =5.378 269 061 ×10^{20}$