sir why cant it be 576? 4*3*4*3*4 ways

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+1 vote

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?

- $120$
- $324$
- $424$
- $576$

+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

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

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