Question

A troupe of 12 dancers is going to line up on stage. Of these dancers, 6 are wearing green and 6 are wearing blue. A dancer wearing green must be in the first position and they must alternate between colors. In how many ways can the dancers line up?

Answer 1

The number of ways that the dancers can line up is; 518400 ways

What is the Fundamental Counting Theorem?

The fundamental counting theorem is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n1 * n2 * n3.....*nₙ

Total = 12

Dancers on Green = 6

Dancers on blue = 6

Number of ways for those wearing green = 6!

Dancers wearing green must be in the first position and so 6 places are left for the blue dancers.

Number of ways to arrange those wearing blue = 6!

Thus;

Number of ways that the dancers can line up = 6! * 6! = 518400 ways

Read more about Fundamental Counting Theorem at; brainly.com/question/26814852

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