There is.... but i need time to think of how to explain it

Number of ways = 6-C-3 = 6! / ( 3! x 3! ) = 20

I would try using the "box method".... as you can see, there are 3 slots available for 6 players. For "player 1" slot, all 6 kids can be chosen. So we will have 6 possible cases for "player 1" slot. For "player 2" slot, we only have 5 kids to choose from, as the sixth child has been chosen to be player 1. For the "player 3" slot, there are only 4 kids left to choose from. Hence, the number of ways to choose 3 kids out of 6 kids, WITH A SPECIFIC ORDER, is given by 6 x 5 x 4 = 120.

Thanks will try to figure out

However, in the case of the question, the order of the 3 players DO NOT MATTER. As you can see below, for any 3 players "denoted by different coloured cubes", there are 6 ways to arrange them. In this question, these 6 methods to group 3 players are all considered as 1 way of grouping. So, Number of ways of grouping = 120 / 6 = 20

Hi Shirley, is this P6 work?

No its P5 work, so tough

Hi, thank you for taking the time to explain. Sorry for being thickheaded but I understood until the 6 x 5 x 4 step. May I ask why is it multiplied? I get that you divide by 6 to get the answer.

Because there are 5 possible ways to select player 2 for each of the 6 possible ways to select player 1. ie you have 6 ways to select player 1. no matter whom is selected as player 1, there will be 5 choices for you to choose player 2, FOR EACH OF THE 6 DIFFERENT WAYS YOU SELECT PLAYER 1.

Oh okay I think I get it now. Thank you very much for your time and help and visual explanation!

I see, I see. Thank you Rye for clearing this up. 👍

Using the branching method....

Each red rectangle shows 1 possible way of choosing the player 1. Since there are 6 kids, There are 6 rectangles. ( 1 kid ---> 1 possibility) Next, each of the possible way of choosing player 1 will lead to 5 possible choices to choose player 2, (denoted by 5 C.) Hence, total number of ways to choose 2 kids from 6 kids, IN AN ORDERED MANNER. is 6 x 5 = 30

Hi, Stella. The key to this question is to use the property that the 3 angles of a triangle add up to 180 degrees. See image for further details. :)

TYSM!! :)

My little girl can understand. Thank you very much

Thks