# In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference

In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference
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Step 1
We can interpret this question as how to split seven students into groups of 3, 2 and 2.
Step 2
The number of ways of partitioning a set of n objects into r cells with n1 elements in the first cell, n2 elements in the second, and so on so forth, is
Therefore, the number of ways that 7 graduate students be assigned to one triple and two double hotel rooms during a conference is:

$=\frac{5040}{24}$
$=210$
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in how many ways can 7 graduate students be assigned to one triple and two double hotel rooms during a conference