Parents of 3 very spoiled children bring home 9 gifts to divide between the kids
ID: 2971424 • Letter: P
Question
Parents of 3 very spoiled children bring home 9 gifts to divide between the kids for Chanukah/Christmas.
The gifts are:
(a) A series of three dierent books on Hunger Games, namely: (1) The Hunger Games, (2) Catching
Fire, and (3) Mockingjay.
(b) Three distint boxes of chocolates.
(c) Three iTune gift cards, each with the value of $50.
The parents at first were planning to divide the gifts in some equitable fashion. But then they decided
to let the children to fight it out!
What is the total number of ways the nine gifts may be divided between three kids without any restriction?
Parents of 3 very spoiled children bring home 9 gifts to divide between the kids for Chanukah/Christmas. The gifts are: A series of three dierent books on Hunger Games, namely: (1) The Hunger Games, (2) Catching Fire, and (3) Mockingjay. Three distint boxes of chocolates. Three iTune gift cards, each with the value of $50. The parents at first were planning to divide the gifts in some equitable fashion. But then they decided to let the children to fight it out! What is the total number of ways the nine gifts may be divided between three kids without any restriction?Explanation / Answer
There are 6 distinct gifts and 3 same gifts (iTune cards)
6 distinct books can be given to children in 3^6 ways = 729 ways.
Now, the three iTune cards can be divided as:
a + b + c = 3
Number of ways = (3+3-1) C (3-1) = 5C2 = 10 ways
Hence, total number of ways = 729 * 10 = 7290
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.