There are 6 flowers in vases in your kitchen. You want to put 3 of them on the dining room table for dinner tonight. Order isn’t important. How many ways can you display the flowers for dinner?

16

This is because 2 coordination  of 3 fit into 6 two times = 2

2 + 2 + 2 + 2 + 2 + 2 +2 + 2 = 16

represents

1- 3  4-6 = 2 set

2-4  6-1  = 2 set

3 -5 6-2 = 2 set

and 3 odds  3 evens = 2 set  

2 odds 1 even  = 1 set

2 evens 1 odd   = 1 set

and other set odds evens   = 2 sets

and other set evens odd etc. etc.  = 2 sets

= 14 sets but there are 16 flower set arrangements altogether.

Step-by-step explanation:

1 2 3

1 2 4

1 2 5

1 2 6

2 3 4

2 3 5

2 3 6

3 4 5

3 4 6

3 4 1

4 5 6

4 5 1

4 5 2

5 6 1

5 6 2

5 6 3

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step-by-step explanation: