2024 DHS P2 Q7

A bakery packs a box of \({10}\) cupcakes comprising \({2}\) red, \({3}\) blue and \({5}\) green ones. The cupcakes are indistinguishable except for their colour.

1. Find the number of ways they can be given to \({10}\) children, if each child is given exactly one cupcake.[1]
2. The bakery packs the \({10}\) cupcakes in a triangular arrangement as shown below.
   
   Find the number of ways to arrange all the cupcakes such that all blue cupcakes are next to each other in the same row.[2]

For another box containing \({10}\) brown identical cupcakes, the bakery decides to spell out the word DELECTABLE by using whipped cream to write one letter on each cupcake.

3. Find the number of ways the cupcakes can be arranged in a row in which the letters are not in alphabetical order. For example: the three letters ‘BGZ’ is arranged in alphabetical order while ‘GBZ’ is not.[2]
4. How many three-letter code word can be formed from the word DELECTABLE?[3]