what is the probability of spinning all the colors of a 4 color spinner in 5 turns

Question

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Answer 1

    After the first spin, there are 3 available colors.

 

    The probability of getting an available color on the second spin is 3/4.

 

   After the second spin, there are 2 available colors.

  The probability of getting an available color on the third spin is 2/4.

 

   After the third spin, there is only one available color.

  The probability of getting an available color on the fourth spin is 1/4.

 

If that does not happen, then a 5th spin is required, the proabability

of which is again 1/4.

 

3/4 * 2/4 * 1/4 * 1/4 = 6/256 = 3/128