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A new flag of ISI club is to be designed with $5$ vertical strips using some or all of the four colors: green, maroon, red and yellow. In how many ways this can be done so that no two adjacent strips have the same color?

  1. $120$
  2. $324$
  3. $424$
  4. $576$
in Combinatory by | 216 views

1 Answer

+2 votes
Color for first strip can be selected from 4 colors in 4 ways.

Color for next strip can be selected in 3 ways(since we can't allow adjacent strips to have same color)

For similar reason, color for each of the next 3 strips can be selected in 3 ways .

Hence total number of ways of coloring the strips of the flag = $4*3*3*3*3$ = $324$ ways
sir why cant it be 576? 4*3*4*3*4 ways

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