Question

In the mountainous regions of India, China, Nepal and Bhutan, it is common to see prayer flags. Each flag has a prayer written on it, and the colour is used to symbolize different elements: green for water, yellow for earth, white for air/wind, blue for sky/space and red for fire. How many different ways Dorji select one or more of the same prayer using these 9 flags: 1 green, 1 yellow, 2 white, 3 blue and 2 red?

Answer 1

Dorji can select one or more of the same prayer using these 9 flags in 28 different ways.

Step-by-step explanation:

To find the number of different ways Dorji can select one or more of the same prayer using these 9 flags, we can use the concept of combinations. We need to find the sum of all possible combinations of 1, 2, and 3 prayers from each color.

Using the combination formula, the number of ways to choose 1 or more prayers from each color:

Green: 1 way

Yellow: 1 way

White: C(2, 1) + C(2, 2) = 2 ways

Blue: C(3, 1) + C(3, 2) + C(3, 3) = 7 ways

Red: C(2, 1) + C(2, 2) = 2 ways

Now, we multiply the number of ways for each color:

1 * 1 * 2 * 7 * 2 = 28 ways

Therefore, Dorji can select one or more of the same prayer using these 9 flags in 28 different ways.