+306 If I buy 7 identical bags of candy for 3 friends, how many ways can I distribute the candy to my 3 friends so that each friend receives at least 1 bag of candy?
If I buy 7 distinguishable postcards, how many ways can I send the postcards to my 3 friends so that each friend receives at least 1 postcard?
+128475 (a) While travelling abroad, I bought 7 identical bags of candy for 3 friends. How many ways can I distribute the candy to my 3 friends, so that each friend gets at least one bag of candy?
This is similar to distributing 7 identical balls into 3 distinct boxes with the restriction that each box must contain at least 1 ball
The number of ways is given by
C (7-1, 3 - 1) = C ( 6,2) = 15 ways
+128475 (b) I also bought 7 different postcards. How many ways can I send the postcards to my 3 friends, so that each friend gets at least one postcard?
Let k be the number of postcards and n be the number of friends
The number of ways =
S (k, n) * n!
Where S(k, n) is a Stirling Number of the Second Kind
So we have
S(7,3) * 3! =
301 * 6 =
1806 ways
