SOLUTION: in how many ways could 18 people be divided into five groups​ containing, respectively 2,5​, 6​, 1​, and 4​,​people? The groups can be chosen in enter your response

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Question 1188651: in how many ways could 18 people be divided into five groups​ containing, respectively 2,5​, 6​, 1​, and 4​,​people?
The groups can be chosen in
enter your response here ways.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are at least two distinct ways to calculate this number.

(1) Choose the groups one group at a time:
choose 2 of the 18 for the first group;
choose 5 of the remaining 16 for the second;
choose 6 of the remaining 11 for the third;
choose 1 of the remaining 5 for the fourth; and
choose 4 of the remaining 4 for the last:

C%2818%2C2%29%2AC%2816%2C5%29%2AC%2811%2C6%29%2AC%285%2C1%29%2AC%284%2C4%29=1543782240

(2) Using multinomial coefficients:

18%21%2F%28%282%21%29%285%21%29%286%21%29%281%21%29%284%21%29%29=1543782240