Suppose I have a supply of 45 textbooks to distribute to a c

Suppose I have a supply of 45 textbooks to distribute to a class of 45 students (one book each). If I have 15 copies of the rst edition, 20 copies of the second edition, and 10 copies of the third edition, in how many dierent ways could these be distributed to the class?

Solution

Use multinomial theorem. Total number of ways in which 45 books can be arranged amongst 45 students is 45!. Now, since there are 15, 20 and 10 copies of first, second and third edition, we must omit out the possible arrangements. This can be done by dividing the total by (15! x 20! x 10!)

Thus, total answer is:

45! / (15! x 20! x 10!)