Question

In a school, 5 colours are allotted to each house. If the flag of Tagore House has to be a sequence of three blocks of different colours, how many flags can they choose from?

• A. 9
• B. 27
• C. 60
• D. 20
• E. 15

Hint:

Distinct blocks → ordered selection without repetition → use permutations: \(^{n}P_{r} = n \times (n-1) \times \cdots\).

Answer 1

The Correct Option is C

Step 1: Choose first block colour.
We have 5 possible colours.

Step 2: Choose second block colour.
Must be different from the first. Hence 4 options.

Step 3: Choose third block colour.
Must be different from both first and second. Hence 3 options.

Step 4: Multiply choices.
Total flags \(= 5 \times 4 \times 3 = 60\).

Final Answer:
\[ \boxed{60} \]