Answer to Question #103891 in Statistics and Probability for nicole

Question

In how many ways can 9 people cross a river riding 3 bancas whose maximum capacity is 2, 4 and 5 respectively?

Answer 1

As per the given question,

Total number of people =9

Total bancas=3

Maximum capacity =2, 4, 5

possible distributions into bancas are

{ 0,4,5} , {1,3,5} , {1,4,4} , {2,2,5} , {2,3,4} , {2,4,3}

So, the required possible ways $=9C_0\times9C_4+9C_1\times8C_3+9C_1\times8C_4+9C_2\times 7C_2+9C_2\times 7C_3+9C_2\times 7C_4$

$=(126+504+630+756+1260+1260)$

$=4536$