Kwanzaa is an African American holiday celebrated December 26th through January 1st. The colors of Kwanzaa are red, green, and black, and the holiday has seven symbolic elements. Two of these elements are the mishumaa saba (the seven candles) and the kinara (the candle holder). Traditionally, the mishumaa saba are arranged in the kinara as shown, three identical red candles on the left, three identical green candles on the right and a black candle in the center. If, however, the candles could be arranged in any order, in how many different ways could the seven candles be arranged in the kinara?

Step-by-step explanation:

Another very interesting problem

If the candles were all of a different color, then the first candle (randomly chosen) would be 7. The second candle would be any one of 6. Third would be any one of the remaining 5, then 4 then 3 then 2 then 1

The abbreviated way of writing that is 7! which means that the number of different ways would be

7*6*5*4 * 3*2*1

However this problem is not that simple The complexity comes from the fact that there are colors that are duplicated.

That event is handled by dividing 7! / by 3! and another 3!

The result is 140

3! = 3*2*1 = 6

So you would take 7! and divide by 6*6

5040/36 = 140

This problem is much more difficult than any of the others.