Try this problem from ISI MStat 2018 PSA Problem 14 based on all possible colorings. We provide sequential hints to help you solve the problem.
A flag is to be designed with 5 vertical stripes using some or all of the four colours: green, maroon, red and yellow. In how many ways can this be done so that no two adjacent stripes have the same colour?
Basic counting principles
But try the problem first...
Answer: is 324
ISI MStat 2018 PSA Problem 14
A First Course in Probability by Sheldon Ross
First hint
How many ways you can colour the first stripe and the second stripe?
You have 4 colour options for the first stripe.
You have (4-1) = 3 colour options for the second stripe.
\( 4 \times 3 \).
Second Hint
How many ways you can colour the third stripe and the rest of the stripes?
You have (4-1) = 3 colour options for the second stripe.
You have (4-1) = 3 colour options for the fourth stripe.
You have (4-1) = 3 colour options for the fifth stripe.
Final Step
Therefore, total number of ways to colour = \( (4 \times 3) \times 3 \times 3 \times 3 = 324 ) \)
From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:
