2021 EJC J2 MYE P2 Q9

Mary holds a party for her son’s birthday. She has invited her son’s friends consisting of \(6\) boys and \(4\) girls to the party. She wants to take a picture of the \(10\) children standing in a row.

1. How many ways can the \(10\) children be arranged in a row if the \(4\) girls are next to each other and the \(6\) boys are next to each other?[1]
2. Mary then asks the \(6\) boys, all of different heights, to arrange themselves in order of their heights, ascending from left to right, but they need not stand together. The girls are free to stand anywhere. In how many ways can the \(10\) children be arranged?[2]

To play a game, the \(10\) children are divided into two equal groups of five each. Find the number of ways that this can be done

3. without restriction.[1]
4. if there must be at least one boy and one girl in each group.[2]

In the game, the children must arrange the nine letters in the word CHALLENGE in a circle randomly.

5. What is the probability that no two adjacent letters are identical?[3]