document.write( "Question 1195029: How many ways are there to distribute 15 district objects into 5 distinct boxes with:
\n" ); document.write( "i) At least three empty box
\n" ); document.write( "ii) No empty box \n" ); document.write( "
Algebra.Com's Answer #827362 by greenestamps(13200)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "i) (part 1): 5 empty boxes

\n" ); document.write( "Obviously that can't be done... 0 ways

\n" ); document.write( "i) (part 2): 4 empty boxes

\n" ); document.write( "Choose 1 of the 5 boxes to be the one that is not empty: 5 ways
\n" ); document.write( "For each of the objects, there is only 1 choice for which box to go into: 1^15 = 1 way
\n" ); document.write( "Number of ways: 5*1 = 5

\n" ); document.write( "i) (part 3): 3 empty boxes

\n" ); document.write( "Choose 2 of the 5 boxes to be the ones that are not empty: C(5,2) = 10 ways
\n" ); document.write( "Each of the 15 items can go in either of 2 boxes: 2^15 ways:
\n" ); document.write( "Number of ways: 10*2^15

\n" ); document.write( "i) ANSWER: 5 + 10*2^15

\n" ); document.write( "ii) Since no box can be empty, first put one object into each of the 5 boxes: C(15,1)*C(14,1)*C(13,1)*C(12,1)*C(11,1) = 15*14*13*12*11 ways
\n" ); document.write( "Each of the remaining 10 objects can be put in any of the 5 boxes: 5^10 ways

\n" ); document.write( "ii) ANSWER: (15*14*13*12*11) * 5^10

\n" ); document.write( " \n" ); document.write( "
\n" );